Question

Suppose a man is trying to decide how to invest $2500 for 25 years. He can invest the money in a CD with an interest rate of 2.2% compounded quarterly. Alternatively, he can invest the money in a savings account that earns simple interest. Determine the values of the annual interest rate (r) for the savings account that produce a better investment than the CD. Enter the answer to the nearest hundredth of a percent.

Answer 1

To determine the values of the annual interest rate for the savings account that produce a better investment than the CD, we need to compare the future values of the investments. We can calculate the future value of the investment in the CD using the formula for compound interest.

Step-by-step explanation:

To determine the values of the annual interest rate for the savings account that produce a better investment than the CD, we need to compare the future values of the investments. We can calculate the future value of the investment in the CD using the formula for compound interest:

FV = P(1+r/n)^(nt)

Where FV is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

After calculating the future value of the CD investment, we can compare it to the future value of the investment in the savings account, which can be calculated using simple interest.

Let's assume the savings account has an annual interest rate of r%. The future value of the investment in the savings account can be calculated using the formula:

FV = P(1 + rt)

We can plug in the given values of $2500 for P, 25 years for t, and 2.2% compounded quarterly for the CD interest rate. We can then compare the future values generated using different values of r for the savings account interest rate. The values of r that produce a higher future value than the CD investment are the ones to be determined.