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Chapter 8: Problem 38

At the time of a child's birth, \(\$ 10,000\) was deposited in an account paying \(5 \%\) interest compounded semiannually. What will be the value of the account at the child's twenty-first birthday?

Short Answer

Expert verified
The value of the account at the child's twenty-first birthday would be the future value obtained from the calculation in step 5.

Step by step solution

01

Understanding the given values

We know that the principal amount \(P = $10,000\), the rate of interest \(r = 5% = 0.05\) (converting percentage to decimal), the number of times it is compounded in a year \(n = 2\) (semiannually means twice a year) and the time period \(t = 21 years\).
02

Formulating the future value formula

Future value formula for compounded interest is \(A = P*(1 + \frac{r}{n})^{n*t}\), where A is the final amount, P is the principal amount, r is the annual interest rate in decimal form, n is the number of compounds per year, and t is the time in years.
03

Substitute the values into the formula

Substitute the given values into the future value formula, \(A = $10,000*(1 + \frac{0.05}{2})^{2*21}\).
04

Calculation

After plugging in the given values into the formula, simplify the equation to calculate A.
05

Solution

Calculate the final value with the given parameters and this will yield the desired solution.

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Most popular questions from this chapter

Describe what is contained in a credit report.

Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit \(\$ 2500\) at the end of each year in an annuity that pays \(6.25 \%\) compounded annually. a. How much will you have saved at the end of 5 years? b. Find the interest.

Suppose that you decide to buy a car for \(\$ 29,635\), including taxes and license fees. You saved \(\$ 9000\) for a down payment and can get a five-year car loan at \(6.62 \%\). Find the monthly payment and the total interest for the loan.

What are credit scores?

Exercises 19 and 20 refer to the stock tables for Goodyear (the tire d. How many shares of this company's stock were traded company) and Dow Chemical given below. In each exercise, use yesterday? the stock table to answer the following questions. Where necessary, e. What were the high and low prices for a share yesterday? round dollar amounts to the nearest cent. f. What was the price at which a share last traded when the stock a. What were the high and low prices for a share for the past exchange closed yesterday? b. If you owned 700 shares of this stock last year, what dividend g. What was the change in price for a share of stock from the did you receive? h. Compute the company's annual earnings per share using c. What is the annual return for the dividends alone? How does Annual earnings per share this compare to a bank offering a \(3 \%\) interest rate? $$ =\frac{\text { Yesterday's closing price per share }}{P E \text { ratio }} . $$ $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \text { 52-Week High } & \text { 52-Week Low } & \text { Stock } & \text { SYM } & \text { Div } & \text { Yld \% } & \text { PE } & \text { Vol 100s } & \text { Hi } & \text { Lo } & \text { Close } & \text { Net Chg } \\ \hline 56.75 & 37.95 & \begin{array}{c} \text { Dow } \\ \text { Chemical } \end{array} & \text { DOW } & 1.34 & 3.0 & 12 & 23997 & 44.75 & 44.35 & 44.69 & +0.16 \\ \hline \end{array} $$
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