Future Value.

Kyle has $2,600in cash received for high school graduation gifts from various relatives. He wants to invest it in a certificate of deposit (CD) so that he will have a down payment on a car when he graduates from college in five years. His bank will pay 10% per year, compounded annually, for the five-year CD. How much will Kyle have in five years to put down on his car?

Future value is the amount to which a single sum (such as an investment in a CD) will grow over a period of time at a compound rate of change (such as the rate earned on a CD).

Future value is the amount that a present value will be worth once it grows over a period of time when it earns compound interest and can be calculated using the following formula:

FV=PV×FVIF i,n

The future value can also be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Most calculators are preset for monthly payments, or 12 periods per year (P/Y=12). In this question, the compounding is on an annual basis; therefore, make sure your calculator setting is one period per year (P/Y=1).

Using a financial table to find the future value interest factor in column i row n of the FVIF table:

FV=PV×FVIF 10,5

The Future Value Interest Factors for $1 compounded at 10 percent for 5 periods (Table C-1opens in a new tab) equals 1.611.

Therefore,

FV=$2,600×1.611=$4,188.60

In five years, the amount Kyle will have to put down on his car is $4,188.60.

The future value can also be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Most calculators are preset for monthly payments, or 12 periods per year (P/Y=12). In this question, the compounding is on an annual basis; therefore, make sure your calculator setting is one period per year (P/Y=1). The values are entered as follows:

Input

-2,600 THEN PV

0 THEM PMT

10 THEN I

5 THEN N

CPT FV =4,187.326 --> ROUND $4,187.33

In five years, the amount Kyle will have to put down on his car is $4,187.33.

Note that the difference between the two amounts ($4,188.60 and $4,187.33) is due to rounding, and that the answer calculated using the financial calculator is more accurate. Future Value. Sandra wants to deposit $220 each year for her son. If she places it in an investment account that averages a 9% annual return, what amount will be in the account in 25 years? How much will she have if the account earns 15% a year?

Future value is the amount to which a series of payments (such as a regular deposit into a savings account) will grow over a period of time when it is placed in an account paying compound interest. The future value of a series of payments can be found using the following formula:

FVA=PMT×FVIFA n,i

The future value can also be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Most calculators are preset for monthly payments, or 12 periods per year (P/Y=12). In this question, the compounding is on an annual basis; therefore, make sure your calculator setting is one period per year (P/Y=1).

Using a financial table to find the future value interest factor in column i row n of the FVIF table:

FVIFA i,n = FVIFA 9,25

The Future Value Interest Factors for $1 compounded at 9 percent for 25 periods equals 84.701.

Therefore, FVA=$220×84.701=$18,634.22

If Sandra deposits $220 each year in a savings account that pays 9 percent, the amount that will be in the account in 25 years is $18,634.22.

The future value can also be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Most calculators are preset for monthly payments, or 12 periods per year (P/Y=12). In this question, the compounding is on an annual basis; therefore, make sure your calculator setting is one period per year (P/Y=1). The values are entered as follows:

Input

Function*

0 THEN PV

-220 THEN PMT

9 THEN I

25 THEN N

CPT FV= 18,634.20

If Sandra deposits $220 each year in a savings account that pays 9 percent, the amount that will be in the account in 25 years is $18,634.20.

Note that any difference between the two amounts ($18,634.22 and $18,634.20) is due to rounding, and that the answer calculated using the financial calculator is more accurate.

The future value can also be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Most calculators are preset for monthly payments, or 12 periods per year

(P/Y=12). In this question, the compounding is on an annual basis; therefore, make sure your calculator setting is one period per year

(P/Y=1).

If Sandra deposits $220 each year in a savings account that pays 9 percent, the amount that will be in the account in 25 years is $18,634.20.

Note that any difference between the two amounts ($18,634.22 and $18,634.20) is due to rounding, and that the answer calculated using the financial calculator is more accurate.

How much will she have if the account earns 15% a year?

Using a financial table to find the future value interest factor in column i row n of the FVIF table:

FVIFA i,n = = FVIFA 15,25

The Future Value Interest Factors for $1 compounded at 15 percent for 25 periods equals 212.793. Future Value. Luis wants to know how much he will have available to spend on his trip to Belize in three years if he deposits $6,000 today at an annual interest rate of 9%.

Future value is the amount to which a single sum (such as an investment in a CD) will grow over a period of time at a compound rate of change (such as the rate earned on a CD). Future value is the amount that a present value will be worth once it grows over a period of time when it earns compound interest. The future value of a single payment can be found using the following formula:

Future Value = Deposit ×FVIFi,n

The future value can also be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Most calculators are preset for monthly payments, or 12 periods per year (P/Y=12). In this question, the compounding is on an annual basis; therefore, make sure your calculator setting is one period per year (P/Y=1).

Part 2

Using a financial table to find the future value interest factor in column i row n of the FVIF table:

FVIF i,n = FVIF 9,3

The Future Value Interest Factors for $1 compounded at 9 percent for 3 Periods equals 1.295.

Therefore,

Future Value = $6,000 ×1.295=$7,770.00

If he deposits $6,000 today at an annual interest rate of 9 percent, the amount Luis will have available to spend on his trip to Belize in three years is $7,770.00.

The future value can also be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Most calculators are preset for monthly payments, or 12 periods per year (P/Y=12). In this question, the compounding is on an annual basis; therefore, make sure your calculator setting is one period per year (P/Y=1). The values are entered as follows:

Input

Function*

-6,000 PV

0 PMT

9 I

3 N

CPT FV= 7,770.17

If he deposits $6,000 today at an annual interest rate of 9 percent, the amount Luis will have available to spend on his trip to Belize in three years is $7,770.17. Future Value. How much will you have in 48 months if you invest $220 a month at 10% annual interest?

Future value is the amount to which a single sum (such as an investment in a CD) will grow over a period of time at a compound rate of change (such as the rate earned on a CD). Future value is the amount that a present value will be worth once it grows over a period of time when it earns compound interest. The future value of a single payment can be found using the following formula:

Future Value = Deposit ×FVIFi,n

The future value can be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Since the payments are made monthly and the periods are in months, be sure to calculate the monthly interest rate by dividing the annual rate by 12.

In this question, the compounding is on a monthly basis; however, since the values are all monthly your calculator setting is (P/Y=1).

Using a financial table to find the future value interest factor in column i row n of the FVIF table:

Future Value = Deposit ×FVIF 0.8333333, 48

The Future Value Interest Factors for $1 compounded at 10 percent for 48 Periods equals 58.722.

Future Value = $220×58.722=$12,919

You will have $12,919.

To calculate the monthly interest rate, use the following formula:

Monthly Interest Rate=10%12=0.8333333%

The values are entered as follows:

Input

Function*

0 PV

-220 PMT

0.8333333 I

48 N

CPT FV=12,918.95

You will have $12,918.95. Using Time Value to Estimate Savings. DeMarcus wants to retire with $1 million in savings by the time he turns 62. He is currently 18 years old. How much will he need to save each year, assuming he can get a

7% annual return on his investments?

To calculate the amount DeMarcus will need to save each year, use the following formula:

Annual Payment=Future Value / FVIFAi,n

You can also find the annual payment using a financial calculator. To solve for the payment, you will need to input the values for PV, FV, N, and I.

DeMarcus wants to retire a millionaire, therefore, the FV is $1,000,000. Since DeMarcus is just starting to save, the PV is $0. The annual return he can earn on his investment, I, is 7%

To calculate the number of years DeMarcus will save for, N, use the following formula:

Number of Years until Retirement=Retirement Age−Current Age

Therefore, Number of Years until Retirement= 62−18=44

The number of years DeMarcus will save for, N, is 44 years.

Then, solving for the amount DeMarcus will need to save each year::

Annual Payment=$1,000,000 / FVIFA 7%,44

Annual Payment=$1,000,000 / 266.12 =$3,757.70

The amount DeMarcus will need to save each year, PMT, is $3,757.70.

Using a financial calculator:

I 7

N 44

PV 0

FV 1,000,000

CPT PMT = 3,757.69

The amount DeMarcus will need to save each year, PMT, is $3,757.69. Present Value. Cheryl wants to have $5,200 in spending money to take on a trip to Disney World in three years. How much must she deposit now in a savings account that pays 10% per year to have the money she needs in three years?

Question content area bottom

The present value of a single cash flow today is a single cash flow, FV, discounted back to the present value, PV, at the annual discount rate. To calculate the present value of a future sum, use the following formula:

PV=FV×PVIF i,n

Using a financial table to find the present value interest factor in column i row n of the PVIF table:

PVIF i,n = PVIF 10%,3

The Present Value Interest Factors for $1 compounded at 10 percent for 3 periods equals 0.751.

Therefore,

PV=$5,200×0.751=$3,905.20

To have $5,200 in three years, Cheryl would need to deposit $3,905.20.

Alternatively, the present value, PV, can be found using a financial calculator. To find the PV, you will need the values for FV, PMT, I, and N. In this question, the compounding is on a monthly basis; however, since the values are all monthly your calculator setting is (P/Y=1). The values are entered as follows:

Input

Function

I 10

N 3

PMT 0

FV 5,200

CPT PV= 3,906.84

To have $5,200 in three years, Cheryl would need to deposit $3,906.84.

Part 5

Note that the difference between the two amounts ($3,905.20 and $3,906.84) is due to rounding, and that the answer calculated using the financial calculator is more accurate. Present Value. Juan would like to give his newly born grandson a gift of $11,000 on his eighteenth birthday. Juan can earn 3% annual interest on a certificate of deposit. How much must he deposit now in order to achieve his goal?

The present value of a single cash flow today is a single cash flow, FV, discounted back to the present value, PV, at the annual discount rate. To calculate the present value of a future sum, use the following formula:

PV=FV×PVIF i,n

Part 2

Using a financial table to find the present value interest factor in column i row n of the PVIF table:

PVIF i,n = PVIF 3%,18

The Present Value Interest Factors for $1 compounded at 3 percent for 18 periods equals 0.587.

Therefore,

PV=$11,000×0.587=$6,457.00

In order to given his grandson $11,000 on his eighteenth birthday, Juan needs to deposit $6,457.00.

Alternatively, the present value, PV, can be found using a financial calculator. To find the PV, you will need the values for FV, PMT, I, and N. In this question, the compounding is on a monthly basis; however, since the values are all monthly your calculator setting is (P/Y=1). The values are entered as follows:

Input

Function

I 3

N 18

PMT 0

FV 11,000

CPT PV = 6,461.34

In order to given his grandson $11,000 on his eighteenth birthday, Juan needs to deposit $6,461.34.

Note that the difference between the two amounts ($6,457.00 and $6,461.34) is due to rounding, and that the answer calculated using the financial calculator is more accurate. To determine the cash option payout, use the present value of a future annuity sum formula:

PVA=PMT×PVIFAi,n

To calculate the annual payment, PMT, use the following formula:

Annual Payment=$30,000,000 / 15=$2,000,000.00

The annual payment is $2,000,000.00.

Annual Payment (PMT) = PVA / N

Using a financial table to find the present value interest factor in column i row n of the PVIF table:

PVIFAi,n= PVIFA11%,15

The Present Value Interest Factors for $1 compounded at 11 percent for 15 periods equals 7.191.

Therefore,PV=$2,000,000.00×7.191=$14,382,000.00

The cash option payout would be $14,382,000.00.

Alternatively, the present value, PV, can be found using a financial calculator. To find the PV, you will need the values for FV, PMT, I, and N. In this question, the compounding is on a monthly basis; however, since the values are all monthly your calculator setting is (P/Y=1). The values are entered as follows:

Input

Function

I= 11

N=15

PMT=2,000,000.00

FV=0

CPT PV= 14,381,739.15

The cash option payout would be $14,381,739.15. $13,136,270.97

(WORK

Annual Payment (PMT) = PVA / N

PMT= 24,000,000 / 22 = 109090.091

PVA=PMT×PVIFAi,n

FV= 0

I =6

N= 22

PMT= 24,000,000 / 22 = 109090.091

CPT PV = $13,136,270.96530 -->$13,136,270.97) $12,462,210.34

(WORK

Annual Payment (PMT) = PVA / N

PMT= 20,000,000 / 20 = 1000000

PVA=PMT×PVIFAi,n

FV= 0

I= 5

N= 20

PMT= 20,000,000 / 20 = 1000000

CPT PV = $12,462,210.34254 -->$12,462,210.34) Future Value of Annuity. Michelle is attending college and has a part-time job. Once she finishes college, Michelle would like to relocate to a metropolitan area. She wants to build her savings so that she will have a "nest egg" to start her off. Michelle works out her budget and decides she can afford to set aside $210 per month for savings. Her bank will pay her 8% per year, compounded monthly, on her savings account. What will be Michelle's balance in five years?

Question content area bottom

Future value is the amount to which a series of payments (such as a monthly contribution to a savings account) will grow over a period of time when it earns compound interest.

The future value can be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Since the payments are made monthly and the periods are in months, be sure to calculate the monthly interest rate by dividing by 12. In this question, the compounding is on a monthly basis; however, since the values are all monthly your calculator setting is (P/Y=1).

To calculate the monthly interest rate, use the following formula:

Monthly Interest Rate= 8% / 12=0.6667%

Monthly Interest Rate= I / 12 = #%

Therefore,

Input

Function*

PV= 0

PMT = -210

I= 0.6667

N = 60

CPT FV= 15,430.30

In five years, Michelle's balance will be $15,430.30. Future Value of Annuity. Twins Jessica and Joshua, both 25, graduated from college and began working in the family restaurant business. The first year, Jessica began putting $2,000 per year in an individual retirement account and contributed to it for a total of 12 years. After 12 years she made no further contributions until she retired at age 65. Joshua did not start making contributions to his individual retirement account until he was 39, but he continued making contributions of $2,000 each year until he retired at age 65. Assuming that both Jessica and Joshua receive 6% interest per year, how much will Jessica have at retirement? How much did she contribute in total? How much will Joshua have at retirement? How much did he contribute in total?

Future value is the amount to which a series of payments (such as a monthly contribution to a savings account) will grow over a period of time when it earns compound interest.

FVA=PMT×FVIFA i,n

FVA=PMT×FVIFA6,12

The Future Value Interest Factors for $1 Annuity compounded at 6 percent for 12 periods (Table B-3) equals 16.870.

FVA (Jessica) = $2,000×16.870 = $33,740.00

This $33,740.00 is then compounded at 6 percent per year for 28 years, since Jessica will leave the money in the IRA until retirement:

FV=PV×FVIF 6,28

FV=PV×FVIF 6,28

The Future Value Interest Factors for $1 compounded at 6 percent for 28 periods (Table B-1) equals 5.112.

FV (Jessica) = $33,740.00×5.112 = $172,479

Alternatively, the future value of an annuity can be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. In this question, the compounding is on a monthly basis; however, since the values are all monthly your calculator setting is (P/Y=1).

Using a financial calculator, Jessica's contributions for 12 years:

PV = 0

PMT= -2,000

I= 6

N=12

CPT FV = 33,739.88

This $33,739.88 is then compounded at 6 percent per year for 28 years, since Jessica will leave the money in the IRA until retirement. To find the FV, you will need the values for PV, PMT, I, and N. In this question, the compounding is on a monthly basis; however, since the values are all monthly your calculator setting is (P/Y=1).

Using a financial calculator:

PV=33,739.88

PMT= 0

I= 6

N=28

CPT FV = 172,468

At retirement, Jessica will have $172,468 and she will have contributed a total of $24,000. Total contributions for Jessica ($24,000) are the equal to the contribution ($2,000) times the number of payments (12).

Now, calculate the amount Joshua will have at retirement.

Future value is the amount to which a series of payments (such as a monthly contribution to a savings account) will grow over a period of time when it earns compound interest.

FVA=PMT×FVIFAi,n

FVA=PMT×FVIFA 6,26

The Future Value Interest Factors for $1 Annuity compounded at 6 percent for 26 periods (Table B-3)) equals 59.156.

FVA (Josh) = $2,000×59.156 = $118,312

Alternatively, the future value of an annuity can be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. In this question, the compounding is on a monthly basis; however, since the values are all monthly your calculator setting is (P/Y=1).

Using a financial calculator, Joshua's contributions for 26 years:

PV= 0

PMT= -2,000

I=6

N=26

CPT FV = 118,313

At retirement, Joshua will have $118,313 and he will have contributed a total of $52,000.

Total contributions for Josh ($52,000) are the equal to the contribution ($2,000) times the number of payments (26). Estimating the Annuity Amount. Amy and Vince want to save $11,000 so that they can take a trip to Europe in four years. How much must they save each month to have the money they need if they can get an annual interest rate of 12%, compounded monthly, on their savings?

The monthly payment can be found using a financial calculator. To find the PMT, you will need the values for PV, FV, I, and N. Since the payments will be made monthly, interest is compounded monthly, so the interest rate must be divided by 12. Be sure to multiple the number of years by 12 to get the number of months. In this question, the compounding is on a monthly basis; however, since the values are all monthly your calculator setting is (P/Y=1).

Although the result the calculator returns may be a negative number, the amount should be stated as a positive value.

The number of periods, N, is calculated by multiplying the number of years by 12, as shown below:

Number of Periods=4×12=48

The number of periods is 48 months.

To calculate the monthly interest rate, I, use the following formula:

Monthly Interest Rate=12% / 12=1.0000%

The monthly interest rate is 1.0000%.

Using a financial calculator, the values are as follows:

Input

Function*

PV = 0

FV= 11,000

I= 1.0000

N= 48

CPT PMT

The amount Amy and Vince will need to save each month is $179.67. Ethical Dilemma. Cindy and Jack have always practiced good financial habits, in particular, developing and living by a budget. They are currently in the market to purchase a new car and have budgeted $300 per month for car payments.

While visiting a local dealership, a salesman, Scott, shows them a car that meets their financial requirements. Then he insists that they look at a much more expensive car that he knows they would prefer. The more expensive car would result in payments of $500 per month.

In discussing the two cars, Cindy and Jack tell Scott that the only way they can afford a more expensive car would be to discontinue making a $200 monthly contribution to their retirement plan, which they have just begun. They plan to retire in 30 years. Scott explains that they would only need to discontinue the $200 monthly payments for five years, that is, the length of the car loan. Scott calculates that the $12,000 in lost contributions over the next five years could be made up over the remaining 25 years by increasing their monthly contribution by only $40 per month, and they would still be able to achieve their goal.

a. Comment on the ethics of a salesperson who attempts to talk customers into spending more than they had originally planned and budgeted.

a. Scott, the salesman, has behaved: (Select the best answer below.)

A. in an ethical way since his obligation is to sell cars.

B. deceitfully since Cindy and Jack will trust him.

C. as though he were their friend.

D. irresponsibly since he should have encouraged them to spend even less. Ethical Dilemma. Cindy and Jack have always practiced good financial habits, in particular, developing and living by a budget. They are currently in the market to purchase a new car and have budgeted $300 per month for car payments.

While visiting a local dealership, a salesman, Scott, shows them a car that meets their financial requirements. Then he insists that they look at a much more expensive car that he knows they would prefer. The more expensive car would result in payments of $500 per month.

In discussing the two cars, Cindy and Jack tell Scott that the only way they can afford a more expensive car would be to discontinue making a $200 monthly contribution to their retirement plan, which they have just begun. They plan to retire in 30 years. Scott explains that they would only need to discontinue the $200 monthly payments for five years, that is, the length of the car loan. Scott calculates that the $12,000 in lost contributions over the next five years could be made up over the remaining 25 years by increasing their monthly contribution by only $40 per month, and they would still be able to achieve their goal.

b. Is Scott correct in his calculation that Cindy and Jack can make up the difference in their retirement by increasing their monthly contributions by only $40 per month for the remaining 25 years?

(Note: Assume an annual rate of return of 6% on Cindy and Jack's investment and assume that hey make investments annually.)

b. Scott's calculation of the future value of the foregone contributions is

a) too high

b) correct

c) too low Future Value of Annuity. Lena has just become eligible to participate in her company's retirement plan. Her company does not match contributions, but the plan does average an annual return of

8%. Lena is 40 and plans to work to age 65. If she contributes

$270 per month, how much will she have in her plan at retirement?

Future value is the amount to which a series of payments (such as a monthly contribution to a savings account) will grow over a period of time when it earns compound interest.

To find the FV, you will need the values for PV, PMT, I, and N.

Interest is compounded monthly, so the interest rate must be divided by 12. Since the contributions are made monthly and the interest compounds monthly, be sure to multiple the number of years by 12 to get the number of months.

In this question, the compounding is on a monthly basis; however, since the values are all monthly your calculator setting is (P/Y=1). Although the result the calculator returns may be a negative number, the amount should be stated as a positive value.

To calculate the number of periods, N, use the following formula:

Number of Periods=(65−40)×12=300

There are 300 months, or periods, in the 25 years untl Lena's retirement.

To calculate the monthly interest rate, I, use the following formula:

Monthly Interest Rate=8% / 12=0.6667%

The monthly interest rate is 0.6667%.

Using a financial calculator, the values are as follows:

PV=0

PMT= -270

I=0.6667

N=300

CPT FV= 256,793.82

When Lena retires, the amount she will have in her retirement plan is $256,793.82. Future Value of Annuity. Stacey would like to have $1 million available to her at retirement. Her investments have an average annual return of 7%. If she makes contributions of $215 per month, will she reach her goal when she retires in 45 years?

Future value is the amount to which a series of payments (such as a monthly contribution to a retirement investment) will grow over a period of time when it is placed in an account paying compound interest. The future value of a series of payments can be found using the following equation:

FVA=PMT×FVIFAi,n

Alternatively, the future value of an annuity can be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Interest is compounded monthy, so the interest rate must be divided by 12. Since the contributions are made montly and the interest compounds monthly, be sure to multiple the number of years by 12 to get the number of months. In this question, the compounding is on a monthly basis; however, since the values are all monthly your calculator setting is (P/Y=1). Although the result the calculator returns may be a negative number, the amount should be stated as a positive value.

To calculate the number of periods, N, use the following formula:

Number of Periods=45×12=540

The number of periods is 540 months.

To calculate the monthly interest rate, I, use the following formula:

Monthly Interest Rate=7% / 12=0.5833%

The monthly interest rate is 0.5833%.

The values are entered as follows:

PV=0

PMT= -215

I=0.5833

N=540

CPT FV=815,407.86

The future value, FV, of Stacey's investments is $815,407.86.

Stacey will reach her goal if there is at least $1,000,000 in her retirement investments when she retires:

FVA(Retirement Investment)≥1,000,000

Stacey will not reach her goal if there is less than $1,000,000 in her retirement investments when she retires:

FVA(Retirement Investment)<1,000,0000

Since the future value is less than $1 million, Stacey will not meet her goal. In order to accumulate $1 million, she must contribute $263.67 per month. Future Value of Annuity. Jesse has just learned that she won $1 million in her state lottery. She has the choice of receiving a lump-sum payment of $450,000 or $100,000 per year for the next 10 years. Jesse can invest the lump sum at 13%, or she can invest the annual payments at 11%. Which should she choose for the greatest return after 10 years?

Future value is the amount to which a single sum (such as a lump-sum investment) will grow over a period of time at a compound rate of change (such as the rate earned on an investment). The future value of a single sum can be found using the following formula:

FV=PV×FVIFi,n

Part 2

Using a financial table to find the future value interest factor in column i row n of the FVIF table:

FV = PV×FVIF13,10

The Future Value Interest Factors for $1 compounded at 13% for 10 periods (Table C-1opens in a new tab) equals 3.395.

Therefore, FV=$450,000×3.395=$1,527,750.00

The future value, FV, of the lump-sum is $1,527,750.00.

Alternatively, the future value of a lump sum can be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. In this question, the compounding is on a annual basis; therefore, be sure your calculator setting is (P/Y=1). The values are entered as follows:

PV=-450,000

PMT=0

I=13

N=10

CPT FV= 1,527,555.33

The future value, FV, of the lump-sum is $1,527,555.33.

Note that the difference between the amount found using the tables and the amount found using the financial calculator is due to rounding, and that the answer calculated using the financial calculator is more accurate.

You now know how much Jesse will have in 10 years if she invests the lump-sum payment option. Next, calculate the amount Jesse will have if she reinvests the annual payments for 10 years and compare the results.

Future value is the amount to which a series of payments (such as a monthly contribution to a savings account) will grow over a period of time when it earns compound interest. To calculate the future value of the payments (annuity), use the following formula:

FVA=PMT×FVIFAi,n

Using a financial table to find the future value interest factor in column i row n of the FVIFA table:

FVA=PMT×FVIFA 11,10

The Future Value Interest Factors for $1 Annuity compounded at 11 percent for 20 periods (Table C-3opens in a new tab) equals 16.722.

Therefore, FVA=$100,000×16.722=$1,672,200.00

The future value, FV, of the annual payments is $1,672,200.00.

Alternatively, the future value of an annuity can be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. In this question, the compounding is on a annual basis; therefore, be sure your calculator setting is (P/Y=1). The values are entered as follows:

PV=0

PMT= -100,000

I= 11

N=10

CPT FV= 1,672,200.90

The future value, FV, of the annual payments is $1,672,200.90.

The annual payment option results in a future value in 10 years of $1,672,200.00, which is more than the $1,527,750.00 Jesse would have with the lump−sum option. Future Value of Annuity. Jen spends $10 per week on doughnuts and coffee. If she takes the same amount that she spends on doughnuts and coffee and invests it each week for the next five years at 10%, compounded weekly, how much will she have in five years?

The future value of an annuity can be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N.

Since payments will be made on a weekly basis, be sure to multiple the number of years by 52. The annual interest rate given will need to be divided by 52, in order to calculate the compunding on a weekly basis. Since you have converted the values to account for the weekly basis, your calculator setting is (P/Y=1).

To calculate the number of periods, N, use the following formula:

Number of periods=5 years×52=260 weeks

To calculate the weekly interest rate, I, use the following formula:

Weekly interest rate=10% / 52=0.1923%

The values are entered as follows:

PV=0

PMT= -10

I=0.1923

N=260

CPT FV = 3,369.24

In five years, Jen will have $3,369.24. Future Value of Annuity. Kirk can take his $1,600 income tax refund and invest it in a 36-month certificate of deposit at 11%, compounded monthly, or he can use the money to purchase a home entertainment system and put $44 a month in a bank savings account that will pay him 12% annual interest. Which choice will give him more money at the end of three years?

The future value of a lump sum can be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Since interest is compounded on a monthly basis, the annual interest rate given will need to be divided by 12 and the number of years will need to be multipled by 12. Since you have converted the values to account for the monthly compounding, your calculator setting is (P/Y=1).

First, calculate the future value, FV, of the depositing the $1,600 income tax return into a 36-month certificate of deposit option.

To calculate the number of periods, N, use the following formula:

Number of Periods=3×12=36

The number of periods is 36 weeks.

To calculate the monthly interest rate, I, use the following formula:

Monthly Interest Rate=11%12=0.9167%

The monthly interest rate is 0.9167%.

The values are entered as:

Input

Function*

PV = -1,600

PMT= 0

I = 0.9167

N=36

CPT FV = 2,222.21

If he put the money into a 36-month certificate of deposit at 11 percent, he will have $2,222.21.

Next, calculate the future value, FV, of the monthly saving option of depositing $44 per month.

The future value of an annuity can be found using a financial calculator. To find the FV, you will need the values for PV, PMT, I, and N. Since interest is compounded on a monthly basis, the annual interest rate given will need to be divided by 12 and the number of years will need to be multipled by 12. Since you have converted the values to account for the monthly compounding, your calculator setting is (P/Y=1).

To calculate the number of periods, N, use the following formula:

Number of Periods=3×12=36.

The number of periods is 36 weeks.

To calculate the monthly interest rate, I, use the following formula:

Monthly Interest Rate=12%12=1%

The monthly interest rate is 1%.

The values are entered as:

Input

Function*

PV= 0

PMT= -44

I= 1

N=36

CPT FV= 1,895.38

With the monthly saving option, he would have $1,895.38 in three years.

Depositing the $1,600 will give him more money at the end of three years.