Question

Jessica wants to accumulate $14,000 by the end of 6 years in a special bank account, which she had opened for this purpose. To achieve this goal, Jessica plans to deposit a fixed sum of money into the account at the end of the month over the 6-year period. If the bank pays interest at the rate of 5% per year compounded monthly, how much does she have to deposit each month into her account?

Answer 1

To accumulate $14,000 by the end of 6 years in a bank account with 5% interest compounded monthly, Jessica needs to deposit approximately $169.22 each month.

Step-by-step explanation:

To calculate how much money Jessica needs to deposit each month into her bank account, we can use the formula for the future value of an annuity:

Future Value = Monthly Deposit × [(1 + Monthly Interest Rate)(Number of Years × Number of Compounding Periods per Year) - 1] / Monthly Interest Rate

In this case, the future value is $14,000 and the interest rate is 5% per year compounded monthly. Since Jessica wants to accumulate this amount over 6 years, there will be 6 × 12 = 72 compounding periods.

Plugging in the values into the formula:

$14,000 = Monthly Deposit × [(1 + 0.05/12)72 - 1] / (0.05/12)

Simplifying the equation, we get:

Monthly Deposit = $14,000 / [(1 + 0.05/12)72 - 1] × (0.05/12)

Using a calculator to evaluate the expression within the brackets, we find:

Monthly Deposit = $14,000 / (1.0041672 - 1) × 0.00417 = $169.22

Therefore, Jessica needs to deposit approximately $169.22 each month into her account to accumulate $14,000 by the end of 6 years.