Answer:
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
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.
