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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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Most popular questions from this chapter

In Exercises 11-14, use the formula $$ A=\frac{P\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]}{\left(\frac{r}{n}\right)} $$ Round all computations to the nearest dollar. Suppose that you drive 40,000 miles per year and gas averages \(\$ 4\) per gallon. a. What will you save in annual fuel expenses by owning a hybrid car averaging 40 miles per gallon rather than an SUV averaging 16 miles per gallon? b. If you deposit your monthly fuel savings at the end of each month into an annuity that pays \(5.2 \%\) compounded monthly, how much will you have saved at the end of six years?

In Exercises 3-4, find the gross income, the adjusted gross income, and the taxable income. Base the taxable income on the greater of a standard deduction or an itemized deduction. Suppose your neighbor earned wages of \(\$ 86,250\), received \(\$ 1240\) in interest from a savings account, and contributed \(\$ 2200\) to a tax-deferred retirement plan. She is entitled to a personal exemption of \(\$ 3800\) and a standard deduction of \(\$ 5950\). The interest on her home mortgage was \(\$ 8900\), she contributed \(\$ 2400\) to charity, and she paid \(\$ 1725\) in state taxes.

Suppose that at age 25 , you decide to save for retirement by depositing \(\$ 50\) at the end of each month in an IRA that pays \(5.5 \%\) compounded monthly. a. How much will you have from the IRA when you retire at age 65 ? b. Find the interest.

A bank bills its credit card holders on the first of each month for each itemized billing. The card provides a 20-day period in which to pay the bill before charging interest. If the card holder wants to buy an expensive gift for a September 30 wedding but can't pay for it until November 5 , explain how this can be done without adding an interest charge.

How much should you deposit at the end of each month into an IRA that pays \(6.5 \%\) compounded monthly to have \(\$ 2\) million when you retire in 45 years? How much of the \(\$ 2\) million comes from interest?
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