CFIN 3 Chapter 4

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"If you invest $500 today in an account that pays 6 percent interest compounded annually, how much will be in your account
after two years?"

\n\n
Using a financial calculator, enter N = 2, I/Y= 6, and PV = -500; compute FV = 561.80"

"What is the present value of an investment that promises to pay you $1,000 in five years if you can earn 6 percent interest
compounded annually?"

\n\n "
Using a financial calculator, enter N = 5, I/Y= 6, and FV = 1,000; compute PV = -747.26"

Compute the present value of $1,552.90 due in 10 years at (a) a 12 percent discount rate and (b) a 6 percent rate.

Using a financial calculator, enter N = 10, I/Y= 6, and FV = 1,552.90; compute PV = -867.13
The present value represents the amount that needs to be invested today at the opportunity cost rate to generate the future amount. In essence, we take the interest out of the future value—that is, discount—to determine the current, or present, value. For this problem, then, if $867.13 is invested today at 6 percent compounded annually, it will grow to $1,552.90 in 10 years.

"To the closest year, how long will it take a $200 investment to double if it earns 7 percent interest? How long will it take if the
investment earns 18 percent?"

\n\n "(1)
PV = -200 400
Using a financial calculator, enter I/Y= 7, PV = -200, PMT = 0, and FV = 400; compute N = 10.24 ≈ 10 years
If I/Y= 18%, N = 4.19 ≈ 4 years"

Which amount is worth more at 14 percent: $1,000 in hand today or $2,000 due in six years?

Using a calculator, enter N = 6, I/Y= 14, PMT = 0, and PV = -1,000; compute FV = 2,194.97
PV = 1,000(1.14)6 = 1,000(2.19497) = 2,194.97
$1,000 today is worth more. The future value of $1,000 at 14 percent over six years is $2,194.97, which is greater than the future $2,000.00.
Alternatively, using a calculator, enter N = 6, I/Y= 14, PMT = 0, and FV = 2,000; compute PV = -911.17
PV = 2,000(1/1.14)6 = 2,000(0.455587) = $911.17
$1,000 today is worth more. The present value of $2,000 at 14 percent over six years is $911.17, which is less than $1,000.00."

"Martell Corporation's sales were $12 million this year. Sales were $6 million five years earlier. To the nearest percentage point, at
what annual rate have sales grown?"

Using a calculator, enter N = 5, PV = -6, PMT = 0, and FV = 12; compute I/Y= 14.87% ≈ 15%."

"If you invest $600 per year for the next 10 years, how much will your investment be worth at the end of 10 years if your
opportunity cost is 10 percent? The first $600 investment will be made at the end of this year."

Using a financial calculator, enter N = 10, I/Y= 10, and PMT = -600; compute FV = 9,562.45"

"If you invest $600 per year for the next 10 years, how much will your investment be worth at the end of 10 years if your
opportunity cost is 10 percent? The first $600 investment will be made today."

Using a financial calculator, switch to BEGIN, enter N = 10, I/Y= 10, and PMT = -600; compute FV = 10,518.70"

"If you want to pay yourself $600 per year for the next 10 years, how much must you deposit today in an investment account that
will pay 10 percent interest annually? The first $600 payment will be withdrawn from the account at the end of this year."

Using a financial calculator, enter N = 10, I/Y= 10, and PMT = -600; compute PV = 3,686.74"

"If you want to pay yourself $600 per year for the next 10 years, how much must you deposit today in an investment account
that will pay 10 percent interest annually? The first $600 payment will be withdrawn from the account today."

\n\n "The general formula for computing the future value of an annuity due is:
0 1 2 3 4 5 6 7 8 9 10
600 600 600 600 600 600 600 600 600 600
PVA(DUE)10 = ?
Using a financial calculator, switch to BEGIN, enter N = 10, I/Y= 10, and PMT = -600; compute PV = 4,055.41
The general formula for computing the future value of an annuity due is:
0 1 2 3 4 5 6 7 8 9 10
600 600 600 600 600 600 600 600 600 600
PVA(DUE)10 = ?
Using a financial calculator, switch to BEGIN, enter N = 10, I/Y= 10, and PMT = -600; compute PV = 4,055.41
The general formula for computing the future value of an annuity due is:
0 1 2 3 4 5 6 7 8 9 10
600 600 600 600 600 600 600 600 600 600
PVA(DUE)10 = ?
Using a financial calculator, switch to BEGIN, enter N = 10, I/Y= 10, and PMT = -600; compute PV = 4,055.41
The general formula for computing the future value of an annuity due is:
0 1 2 3 4 5 6 7 8 9 10
600 600 600 600 600 600 600 600 600 600
PVA(DUE)10 = ?
Using a financial calculator, switch to BEGIN, enter N = 10, I/Y= 10, and PMT = -600; compute PV = 4,055.41
Using a financial calculator, switch to BEGIN, enter N = 10, I/Y= 10, and PMT = -600; compute PV = 4,055.41"

"What is the present value of a perpetuity of $280 per year if the appropriate discount rate is 7 percent? What would happen to
the present value of the perpetuity if the appropriate rate rose to 14 percent?"

\n\n "PVP = $280/0.07 = $4,000. PVP = $280/0.14 = $2,000.
When the interest rate is doubled, the PV of the perpetuity is halved."

"Find the amount to which $500 will grow in five years if the investment earns 12 percent compounded (a) annually, (b)
semiannually, and (c) monthly."

Using a financial calculator, enter N = 5, I/Y= 12, and PV = -500; compute FV = 881.17

Using a financial calculator, enter N = 10, I/Y= 6, and PV = -500; compute FV = 895.42

Using a financial calculator, enter N = 60, I/Y= 1, and PV = -500; compute FV = 908.35"

"While Steve Bouchard was a student at the University of Florida, he borrowed $12,000 in student loans at an annual interest
rate of 9 percent. If Steve repays $1,500 per year, how long, to the nearest year, will it take him to repay the loans?"

\n\n "0 1 2 n-1 n Years
12,000 -1,500 -1,500 -1,500 -1,500
1%
...
...
...
...
...
12%
6%
...
...
...
...
...
r = 9%
...
Solutions
6
−=−=+09.01500,1000,12r1PMTPVAnn)09.1(1)r1(1
Using a calculator, enter I/Y= 9, PV = 12,000, FV = 0, and PMT = -1,500; compute N = 14.77 ≈ 15 years"

"Hilda invested $5,000 four years ago. If the investment is now worth $7,058, what rate of return has Hilda earned on her
investment? Assume that interest is compounded annually."

Using a calculator, enter N = 4, PV = -5,000, PMT = 0, and FV = 7,058; compute I/Y= 9%."

"Jack just discovered that he holds the winning ticket for the $87 million "mega" lottery in Missouri. Now he must decide which
alternative to choose: (a) a $44 million lump-sum payment today or (b) a payment of $2.9 million per year for 30 years. With the
second option, the first payment will be made today. If Jack's opportunity cost is 5 percent, which alternative should he choose?"

alculator: Switch to begin mode, n = 30, I/Y= 5, PMT = 2,900,000, and FV = 0; compute PV = -46,809,113.
Because PVA(DUE) = $46,809,113, which is greater than the lump-sum payment of $44 million, the annuity option should be chosen."

"Your broker offers to sell you a note for $13,250 that will pay $2,345.05 per year for 10 years. If you buy the note, what rate of
interest (to the closest percent) will you be earning?"

Using a calculator, enter N = 10, PV = -13,250, PMT = 2,345.05, and FV = 0; compute I/Y= 12%."

"Brandi just received her credit card bill, which has an outstanding balance equal to $3,310. The credit card carries an 18 percent
simple interest rate, which is compounded monthly. If Brandi pays $150 each month, how long will it take her to pay off the credit
card bill? Assume that the only charge Brandi incurs from month to month is the interest that must be paid on the remaining
outstanding balance."

Calculator solution: I/Y= 18/12 = 1.5, PV = 3,310, PMT = -150, and FV = 0; N = ? = 27.0 months, or 2.2 years."

"Allison wants to pay off her existing automobile loan. Two years ago, Allison borrowed $35,600 with terms that required her to
make monthly payments equal to $739 for a period of five years. The interest rate on the loan is 9 percent. To the nearest dollar, how
much does Allison currently owe on her automobile loan? The most recent payment on the loan was made yesterday."

Calculator solution: N = 36, I/Y= 9/12 = 0.75, PMT = -739, and FV = 0; PV = ? = 23,239."

"If the appropriate interest rate is 8 percent, what are the present values of the following cash flow streams?
Year Cash Stream A Cash Stream B
1 $100 $300
2 400 400
3 400 400
4 300 100"

Using a financial calculator, simply enter the cash flows into the cash flow register (be sure to enter CF0 = 0), enter I/Y= 8, and press the NPV key to find NPV = PV = $973.57 for Cash Stream A. Repeat for Cash Stream B to get NPV = PV = $1,011.75 when I/Y= 8%."

"Savannah, who is a recent college graduate, is making plans to pay back the $46,000 in student loans that she took out during
the past four years. The student loans require Savannah to pay interest equal to 5.4 percent. Payments will be made monthly,
beginning today, and the loans must be repaid within 20 years. Based on this information, how much must Savannah pay each
month?"

\n\n Calculator solution: Switch to begin mode; N = 240, I/Y= 5.4/12 = 0.45, PV = 46,000, and FV = 0; PMT = ? = -312.43.

"Suppose you have been shopping for mortgages to finance the house that you want to buy. The East Coast Federal Credit
Union (ECFCU) has offered a 30-year fixed mortgage that requires you to pay 6 percent interest compounded monthly. The purchase
price of the house is $260,000, and you plan to make a down payment equal to $28,000. What would your monthly payments be with
the ECFCU mortgage?"

\n\n Calculator solution: N = 360, I/Y= 6/12 = 0.5, PV = 232,000, and FV = 0; PMT = ? = -1,390.96.

"In problem 4-22, you should have found that the monthly payment is $1,391. Suppose it is now 10 years later, such that you
have lived in the house for 10 years, and you are considering paying off your mortgage. How much do you owe on the mortgage if
this month's payment was made yesterday?"

Calculator solution: N = 240, I/Y= 6/12 = 0.5, PMT = -1,391, and FV = 0; PV = ? = 194,157."

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