Question

Carmen wants to save money to buy a motorcycle. She invests in an ordinary annuity that earns 7.2% interest, compounded monthly. Payments will be made at the end of each month.

How much money will she need to pay into the annuity each month for the annuity to have a total value of $7000 after 6 years?
Do not round intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.

Answer 1

Explanation:

To find out how much money Carmen needs to pay into the annuity each month, we can use the formula for the future value of an ordinary annuity:

Future Value = Payment Amount * ((1 + Monthly Interest Rate)^(Number of Payments) - 1) / Monthly Interest Rate

In this case:

Future Value = $7,000

Annual Interest Rate = 7.2% = 0.072 (converted to decimal)

Monthly Interest Rate = Annual Interest Rate / 12 = 0.072 / 12

Number of Payments = 6 years * 12 months/year = 72

Plugging in the values into the formula:

$7,000 = Payment Amount * ((1 + (0.072 / 12))^(72) - 1) / (0.072 / 12)

To solve for the Payment Amount, we can rearrange the formula:

Payment Amount = Future Value * (Monthly Interest Rate) / ((1 + Monthly Interest Rate)^(Number of Payments) - 1)

Let's calculate the value:

Payment Amount = $7,000 * (0.072 / 12) / ((1 + (0.072 / 12))^(72) - 1)

Using a calculator or spreadsheet software, we find that the Payment Amount is approximately $71.73 (rounded to the nearest cent).

Therefore, Carmen needs to pay approximately $71.73 into the annuity each month for the annuity to have a total value of $7,000 after 6 years.