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Terms in this set (92)

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.
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.
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​).
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. 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.