An investment offers $5,100 per year, with the first payment occurring one year from now. The required return is 5 percent.

Problem 6-4 Calculating Annuity Present Value [LO1]

An investment offers $5,100 per year, with the first payment occurring one year from now. The required return is 5 percent.

a.    What would the value be today if the payments occurred for 10 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.   
What would the value be today if the payments occurred for 35 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

c.    What would the value be today if the payments occurred for 65 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
d.    What would the value be today if the payments occurred forever? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)


Explanation

Calculator Solution:

   

Enter

10

5%

±$5,100

N

I/Y

PV

PMT

FV

Solve for

$39,380.85

  

Enter

35

5%

±$5,100

N

I/Y

PV

PMT

FV

Solve for

$83,508.39

  

Enter

65

5%

±$5,100

N

I/Y

PV

PMT

FV

Solve for

$97,721.46

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Prescott Bank offers you a five-year loan for $52,000 at an annual interest rate of 8.25 percent. What will your annual loan payment be?

Problem 6-9 Calculating Annuity Values [LO2]
Prescott Bank offers you a five-year loan for $52,000 at an annual interest rate of 8.25 percent. What will your annual loan payment be?


Answer

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

The time line is:

0	1	2	3	4	5
$52,000	C	C	C	C	C

Here we have the PVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the PVA equation:

PVA = C({1 − [1/(1 + r)t]}/r)

$52,000 = C{[1 − (1/1.08255)]/.0825}

We can now solve this equation for the annuity payment. Doing so, we get:

C = $52,000/3.96654

C = $13,109.66

   

Calculator Solution:

  

Enter

5

8.25%

±$52,000

N

I/Y

PV

PMT

FV

Solve for

$13,109.66

Find the EAR in each of the following cases

Problem 6-12 Calculating EAR [LO4]

Find the EAR in each of the following cases (Use 365 days a year. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.):

 

Explanation

For discrete compounding, to find the EAR, we use the equation:

EAR = [1 + (APR/m)]m − 1

EAR = [1 + (.099/4)]4 − 1 = .1027, or 10.27%

EAR = [1 + (.189/12)]12 − 1 = .2063, or 20.63%

EAR = [1 + (.149/365)]365 − 1 = .1606, or 16.06%

To find the EAR with continuous compounding, we use the equation:

EAR = eq − 1

EAR = e.119 − 1

EAR = .1264, or 12.64%

Calculator Solution:

  

Enter	9.9%						4
		NOM			EFF			C/Y
Solve for				10.27%

  

Enter	18.9%						12
		NOM			EFF			C/Y
Solve for				20.63%

   

Enter	14.9%						365
		NOM			EFF			C/Y
Solve for				16.06%