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Chapter 8: Problem 30

To offer scholarships to children of employees, a company invests \(\$ 15,000\) at the end of every three months in an annuity that pays \(9 \%\) compounded quarterly. a. How much will the company have in scholarship funds at the end of 10 years? b. Find the interest.

Short Answer

Expert verified
a. The company will have approximately \$750,101.53 in scholarship funds at the end of 10 years. b. The total interest earned will be approximately \$450,101.53.

Step by step solution

01

- Determine the variables

First, identify the variables required for the calculations: Principal (P) = \$15,000, this is the amount invested every quarter. The annual interest rate (r) = 9%, which when compounded quarterly becomes \(r\div4 = 9\%\div4 = 2.25\%\), this is the interest rate per quarter. The total number of periods (n) = 10 years * 4 quarters = 40, this represents the total number of investments over the 10 year period.
02

- Calculate the future value

The future value (FV) of an annuity can be calculated using the formula \(FV = P *[(1 + r)^n - 1] / r\). Substituting P = \$15,000, r = 2.25\% (in decimal format 0.0225), and n = 40 into the equation, we get: \(FV = 15000 *((1 + 0.0225)^{40} - 1) / 0.0225\)
03

- Calculate the total interest

The total interest is equivalent to the future value minus the total principal paid. The total principal paid is \(P*num\), where \(num\) is the total number of payments made. In this case, \(num\) is 40 because the annuity is paid quarterly for 10 years. So the total interest will be: \(Interest = FV - P*num\)

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