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Chapter 8: Problem 56

How much should you deposit at the end of each month in an IRA that pays \(8 \%\) compounded monthly to earn \(\$ 60,000\) per year from interest alone, while leaving the principal untouched, when you retire in 30 years?

Short Answer

Expert verified
The monthly deposit required in the IRA is $5,000.

Step by step solution

01

Understand the Interest

Firstly, decipher what the return interest rate means. An interest rate of 8% compounded monthly means that each month, the account balance increases by 1/12 of 8%, or approximately 0.67% (0.08/12). This means that the contribution will increase by this rate each month, so the contribution value is important for the total balance.
02

Calculate Yearly Interest

We aim to earn $60,000 per year from interest. Since interest is compounded monthly, we divide the yearly interest by 12 to get the desired monthly interest, which is $5,000 (60,000 / 12).
03

Calculate Monthly Contribution

As we aim to make the principal untouched while gaining interest, that means our monthly contribution should match the interest every month. Hence, the monthly contribution required will be $5,000.
04

Evaluate the Plan

Evaluate if the monthly contribution is realistic and achievable based on personal financial situation. In this case, $5000 per month for 30 years without using any part of the principal.

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Most popular questions from this chapter

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

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? $$ \begin{array}{|l|l|l|l|} \hline \$ ? \text { at the end of each month } & 8.25 \% \text { compounded monthly } & 40 \text { years } & \$ 1,500,000 \\ \hline \end{array} $$

The cost of a home is financed with a $$ 160,00030\(-year fixed-rate mortgage at \)4.2 \%$. a. Find the monthly payments and the total interest for the loan. b. Prepare a loan amortization schedule for the first three months of the mortgage. Round entries to the nearest cent.

Solve for \(P\) : $$ A=\frac{P\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]}{\left(\frac{r}{n}\right)} . $$ What does the resulting formula describe?

Describe two advantages of renting over home ownership.
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