Question

Hamilton is saving for retirement. He deposits $350 each month at 2.7% annual interest for 30 years. According to his calculations, at the end of 30 years he should have $153,847.57 in his account. How much of this did Hamilton contribute and how much of this is interest?

Answer 1

Hamilton contributed $126,000 to his retirement account. The remaining $27,847.57 is the interest earned over the 30-year period, making the total amount in his account at the end of the period equal to $153,847.57.

Step-by-step explanation:

Calculating Contributions and Interest in a Retirement Account

Hamilton is saving for retirement by depositing $350 each month at an annual interest rate of 2.7% for a period of 30 years. To determine how much of the total amount at the end of this period is Hamilton's contribution and how much is due to interest, we need to differentiate between the money he deposited and the interest that accrued over time.

First, let's calculate the total contribution made by Hamilton:
350 dollars per month × 12 months per year × 30 years = $126,000.
This is the amount Hamilton contributed to his retirement savings without taking any interest into account.

Next, we take the future value of Hamilton's account, which is $153,847.57, and subtract the total contributions to find the amount attributed to interest:
$153,847.57 - $126,000 = $27,847.57.

So, Hamilton contributed $126,000 to his retirement fund, and the remaining $27,847.57 is the interest earned over the 30-year period.