Question

To offer scholarships to children ofâ employees, a company invests 10,000 at the end of every three months in an annuity that pays 8.5% compounded quarterly.

a. How much will the company have in scholarship funds at the end of tenâ years?

b. Find the interest.

a. The company will have $... in scholarship funds.

Answer 1

a. $633 849.78; b. $233 849.78

Explanation:

a. Value of Investment

The formula for the future value (FV) of an investment with periodic deposits (p) is

FV =(p/i)(1 + i)[(1 + i)^n -1)/i]

where

i = interest rate per period

n = number of periods

Data:

p = $10 000

APR = 8.5 % = 0.085

t = 10 yr

Calculations:

Deposits are made every quarter, so

i = 0.085/4 = 0.02125

There are four quarters per year, so

n = 10 × 4 = 40

FV = (10 000/0.02125)(1 + 0.02125)[(1 + 0.02125)^40 - 1)]

= 470 588.235 × 1.02125 × (1.02125^40 - 1)

= 480 588.235(2.318 904 06 - 1)

= 480 588.235 × 1.318 904 06

= 633 849.78

The company will have $633 849.78 in scholarship funds.

b. Interest

Amount accrued = $633 849.78

Amount invested = 40 payments × ($10 000/1 payment) = 400 000.00

Interest = $233 849.78

The scholarship fund earned $233 849.78 in interest.