Question

Your birthday is next week and instead of other presents, your parents promised to give you $2,900 in cash. Since you have a part-time job and, thus, don’t need the cash immediately, you decide to invest the money in a bank CD that pays 6.60 percent, compounded quarterly, for the next two years. How much money can you expect to earn in this period of time? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answer to the nearest penny.)

Answer 1

By investing $2,900 in a CD with a 6.60% annual interest rate, compounded quarterly, for two years, the final amount will be approximately $3,313.54. Indeed, this results in about $413.54 in interest earnings over the two-year term.

Step-by-step explanation:

To calculate the amount of money that would be earned by investing $2,900 in a bank CD that pays 6.60 percent, compounded quarterly, for two years, we use the compound interest formula:

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

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount ($2,900).
• r is the annual interest rate (decimal form of 6.60% which is 0.0660).
• n is the number of times that interest is compounded per year (quarterly compounding means n=4).
• t is the time the money is invested for, in years (t=2).

By substituting the terms we get:

A = 2900(1 + 0.0660/4)^(4*2)

A = 2900(1 + 0.0165)^(8)

A = 2900(1.0165)^(8)

A = 2900 * 1.142601

A ≈ $3,313.54

Then, round your final answer to the nearest penny:

A = $3,313.54

The future value of the CD at the end of two years will be approximately $3,313.54, so the interest earned is:

Interest = A - P

Interest = $3,313.54 - $2,900

Interest ≈ $413.54

You can expect to earn around $413.54 in interest from the CD over the two-year period.