Question

1.A loan is offered with monthly payments and a 12.50 percent APR. What’s the loan’s effective annual rate (EAR)?

2. Assume that you contribute $360 per month to a retirement plan for 15 years. Then you are able to increase the contribution to $720 per month for another 25 years. Given a 6.0 percent interest rate, what is the value of your retirement plan after the 40 years?

Answer 1

Part 1:

APR = 12.50%

EAR = (1 + 12.50%/ 12)¹² - 1

EAR = (1.010417)¹² - 1

EAR = 1.132416 - 1

EAR = 13.24%

Part 2:

PMT = 360

N = 15 *12 = 180

I = 6%/ 12 = 0.5%

PV = 0

Using Financial Calculator, the value at end of 15 years

FV = 104,694.74

Now we will calculate future value at end of 40 years.

FV = 104,694.74 * (1 + 0.5%)^{(25 * 12)}

FV = 104,694.74 * 4.4649

FV = 467,458.85

Now will calcualte value of 25 year annuity.

PMT = 720

N = 25 *12 = 300

I = 6%/ 12 = 0.5%

PV = 0

Using Financial Calculator, the value at end of 25 years

FV = 498,955.65

Total value = 498,955.65 + 467,458.85

Total value = 966,414.50