Fuente, Inc., has identified an investment project with the following cash flows.

Problem 6-3 Future Value and Multiple Cash Flows [LO1]
Fuente, Inc., has identified an investment project with the following cash flows.
Year    Cash Flow
1         $    940   
2              1,170   
3              1,390   
4              2,130   


a.   
If the discount rate is 6 percent, what is the future value of these cash flows in Year 4? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b.    If the discount rate is 14 percent, what is the future value of these cash flows in Year 4? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.    If the discount rate is 21 percent, what is the future value of these cash flows in Year 4? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)


Explanation

The time line is:

0	1	2	3	4
	$940	$1,170	$1,390	$2,130

 

To solve this problem, we must find the FV of each cash flow and sum. To find the FV of a lump sum, we use:

FV = PV(1 + r)t

FV@6% = $940(1.06)3 + $1,170(1.06)2 + $1,390(1.06) + $2,130 = $6,037.57

FV@14% = $940(1.14)3 + $1,170(1.14)2 + $1,390(1.14) + $2,130 = $6,627.78

FV@21% = $940(1.21)3 + $1,170(1.21)2 + $1,390(1.21) + $2,130 = $7,190.16

Notice, since we are finding the value at Year 4, the cash flow at Year 4 is added to the FV of the other cash flows. In other words, we do not need to compound this cash flow.

 

Calculator Solution:

CFo	$0	CFo	$0	CFo	$0
C01	$940	C01	$940	C01	$940
F01	1	F01	1	F01	1
C02	$1,170	C02	$1,170	C02	$1,170
F02	1	F02	1	F02	1
C03	$1,390	C03	$1,390	C03	$1,390
F03	1	F03	1	F03	1
C04	$2,130	C04	$2,130	C04	$2,130
F04	1	F04	1	F04	1
I = 6		I = 14		I = 21
NFV CPT		NFV CPT		NFV CPT
$6,037.57		$6,627.78		$7,190.16

Thanks

First Simple Bank pays 9.4 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 9 years?

Problem 6-29 Simple Interest versus Compound Interest [LO4]

First Simple Bank pays 9.4 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 9 years? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer

 

Explanation

The total interest paid by First Simple Bank is the interest rate per period times the number of periods. In other words, the interest by First Simple Bank paid over 9 years will be:

.0940(9) = .846

First Complex Bank pays compound interest, so the interest paid by this bank will be the FV factor of $1 minus the initial investment of $1, or:

(1 + r)9 − 1

Setting the two equal, we get:

.0940(9) = (1 + r)9 − 1

r = 1.8461/9 − 1

r = .0705, or 7.05%

You want to buy a new sports coupe for $85,500, and the finance office at the dealership has quoted you an APR of 6.7 percent for a 72 month loan to buy the car.

You want to buy a new sports coupe for $85,500, and the finance office at the dealership has quoted you an APR of 6.7 percent for a 72 month loan to buy the car.

a.    What will your monthly payments be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.   
What is the effective annual rate on this loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Explanation

We first need to find the annuity payment. We have the PVA, the length of the annuity, and the interest rate. Using the PVA equation:

 

PVA = C({1 − [1/(1 + r)t]}/r)

$85,500 = $C[1 − {1/[1 + (.067/12)]72}/(.067/12)]

Solving for the payment, we get:

C = $85,500/59.15299

C = $1,445.40

To find the EAR, we use the EAR equation:

EAR = [1 + (APR/m)]m − 1

EAR = [1 + (.067/12)]12 − 1

EAR = .0691, or 6.91%

  

Calculator Solution:

  

Enter

72

6.70%/12

±$85,500

N

I/Y

PV

PMT

FV

Solve for

$1,445.40

  

Enter	6.7%						12
		NOM			EFF			C/Y
Solve for				6.91%

Thanks

The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $22,000 per year forever.

Problem 6-11 Calculating Perpetuity Values [LO1]

The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $22,000 per year forever. Suppose a sales associate told you the policy costs $467,000. At what interest rate would this be a fair deal? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Thanks