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.

a. $633 849.78; b. $233 849.78

Step-by-step 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

dа ta:

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.