Question

13. Kevin wants to pay $17,500 each year on his investment account and would like to retire with $2,580,000. Assuming the interest rate for Kevin’s investment account is 11.2% and that it will compound semiannually, how many years will it take before Kevin meets his investment goal of $2,580,000?

14. Part A: Assume you will receive a constant stream of $14,000 each year for 35 years. If the interest rate is 10.5% and it will compound annually, what will be the present value of the annuity?

Part B: What will be your answer to the same question if the same annuity grows by 2.2% each year? Show your work.

Answer 1

13]

First, we calculate the effective annual rate (EAR) of 11.2% compounded semiannually.

EAR = (1 + (r/n))ⁿ - 1

where r = annual nominal rate, and n = number of compounding periods per year

EAR = (1 + (11.2%/2))² - 1 = 11.5136%

Number of years to meet investment goal is calculated using NPER function in Excel :

rate = 11.5136%

pmt = -17500 (Yearly deposit. This is entered with a negative sign as it is a cash outflow)

pv = 0 (Beginning amount in account is zero)

fv = 2580000 (Required ending value of account)

NPER is calculated to be 26.51

It will take 26.51 years

14]

a]

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment. This is $14,000

r = interest rate per period. This is 10.5%.

n = number of periods. This is 35

PV of annuity = $14,000 * [1 - (1 + 10.5%)^-35] / 10.5%

PV of annuity = $129,285.16

b]

Present value of growing annuity = P * [1 - ((1 + g) / (1 + r))ⁿ] / (r - g),

where P = first payment. This is $14,000

r = interest rate per period. This is 10.5%.

n = number of periods. This is 35

g = growth rate = 2.2%

Present value of growing annuity = $14,000 * [1 - ((1 + 2.2%) / (1 + 10.5%))³⁵] / (10.5% - 2.2%)

Present value of growing annuity = $157,706.09