Question

Harvey deposited $6,000 in a new account at his bank.

The bank pays 4.5% interest compounded annually on this account.

Harvey makes no additional deposits or withdrawals.



Which amount is closest to the balance of the account at the end of 6 years?

Answer 1

To calculate the balance of Harvey's account at the end of 6 years with an annual interest rate of 4.5% compounded annually, we can use the formula for compound interest, which is:

\[
A = P(1 + r)^n
\]

where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial deposit).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of years the money is invested or borrowed.

Plugging in the values:
- \(P = 6000\)
- \(r = 4.5\% = 0.045\)
- \(n = 6\)

Now, substitute the values into the formula:

\[
A = 6000(1 + 0.045)^6
\]

Calculating \(1 + 0.045\):

\[
1 + 0.045 = 1.045
\]

Now raise this to the power of 6:

\[
(1.045)^6 \approx 1.283682
\]

Now multiply this by the principal:

\[
A \approx 6000 \times 1.283682 \approx 7690.09
\]

Therefore, the amount closest to the balance of the account at the end of 6 years is approximately **$7,690.09**.