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Chapter 8: Problem 45

Will you earn more interest in one year by depositing \(\$ 2000\) in a simple interest account that pays \(6 \%\) or in an account that pays \(5.9 \%\) interest compounded daily? How much more interest will you earn?

Short Answer

Expert verified
You will earn more interest in an account that pays 5.9% interest compounded daily. The difference in interest earned will be approximately $2.02.

Step by step solution

01

Calculate Simple Interest

First, calculate the amount with simple interest using the formula A=P(1+rt). Substituting the given values we get: A=2000(1+0.06*1)=2120
02

Calculate Compound Interest

Then, calculate the amount with compound interest using the formula A=P(1+r/n)^(nt). Since the interest is compounded daily, n=365. Substituting the known values we will have A=2000(1+0.059/365)^(365*1) which equals to approximately 2122.02.
03

Calculate the difference

The difference in interest earned in a year by depositing in two different accounts is: 2122.02 - 2120 = 2.02

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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?

What is an annuity?

In Exercises 11-18, a. Determine the periodic deposit. Round up to the nearest dollar. b. How much of the financial goal comes from deposits and how much comes from interest? $$ \begin{array}{|l|l|l|l|} \hline \$ ? \text { at the end of every three months } & 4.5 \% \text { compounded quarterly } & 5 \text { years } & \$ 25,000 \\ \hline \end{array} $$

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? $$ =\frac{\text { Yesterday's closing price per share }}{P E \text { ratio }} . $$ $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \text { 52-Week High } & \text { 52-Week Low } & \text { Stock } & \text { SYM } & \text { Div } & \text { Yld \% } & \text { PE } & \text { Vol 100s } & \text { Hi } & \text { Lo } & \text { Close } & \text { Net Chg } \\ \hline 73.25 & 45.44 & \text { Goodyear } & \text { GT } & 1.20 & 2.2 & 17 & 5915 & 56.38 & 54.38 & 55.50 & +1.25 \\ \hline \end{array} $$

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