Question

Suppose you deposit $1,000 in an account today that pays 5% interest, compounded annually. What will be the balance in the account at the end of two years if you withdraw only the interest paid on interest?

1. $1,000.00
2. $1,050.00
3. $1,100.00
4 $1,102.50

Answer 1

After two years, with a 5% interest rate compounded annually and withdrawing only the interest paid on interest, the balance in the account would be $1,100.00.

Step-by-step explanation:

If you deposit $1,000 in an account that pays 5% interest compounded annually, the balance at the end of one year would be the original deposit multiplied by 1.05 (5% interest). Therefore, after one year, your account balance would be $1,000 × 1.05 = $1,050. In the second year, the interest is again 5% on the new balance. This means at the end of the second year, your balance before any withdrawals would be $1,050 × 1.05 = $1,102.50.

Now, if you withdraw only the interest paid on interest, you would take out the interest earned on the original interest from the first year. The first year's interest is $50, and the second year's interest on this amount is 5% of $50, which is $2.50. Therefore, after withdrawing the $2.50, the ending balance would be $1,102.50 – $2.50 = $1,100.