Annuities
Suppose a fixed investment R is done every fixed number of periods m per year for t years at a constant rate r.
a.
The final value of the investments plus the interest is calculated as follows:
Where:
n = number of total periods of the investment.
n = m*t
The company invests R = $13,000 for t = 10 years at the end of every quarter (3 months), thus m = 4. The interest rate is r = 9% = 0.09.
The interest rate compounds quarterly.
Calculate:
n = 4*10 = 40
i = 0.09 / 4 = 0.0225
Calculating:
FV = $829,220
The company will have $829,220 in scholarship funds
b. The interest can be found by subtracting the final value and the initial value. We have to calculate the latter:
Thus, the interest is:
welcI = $829,220 - $340,516
I = $488,704
The interest is $488,704