Question

James deposited $575 into a bank account that earned 5.5% simple interest each year. No money was deposited into or withdrawn from the account.

How much money was in the account after ​ ​ 212 ​ ​ years?

Round your answer to the nearest cent.

Enter your answer in the box.

Answer 1

Explanation:

Since the interest is simple interest, the interest earned each year is calculated as a percentage of the initial deposit. After 1 year, the amount of interest earned would be:

$575 x 5.5% = $31.63

Therefore, the balance in the account after 1 year would be:

$575 + $31.63 = $606.63

After 2 years, the interest earned would again be:

$575 x 5.5% = $31.63

So the balance in the account after 2 years would be:

$606.63 + $31.63 = $638.26

We can repeat this process for each year up to 212 years. However, since the interest rate is the same every year, we can simplify the calculation by multiplying the initial deposit by (1 + 0.055n), where n is the number of years. Therefore, the balance after 212 years would be:

$575 x (1 + 0.055 x 212) = $136,396.00

Rounding to the nearest cent, the balance after 212 years would be $136,396.00.