Question

Suppose Patrick Goldsmith deposited $1000 in an account that earned simple interest at an annual rate of 10% and left it there for 5 years. At the end of the 5 years, Patrick deposited the entire amount from that account into a new account that earned 10% compounded quarterly. He left the money in this account for 5 years. How much did he have after the 10 years? (Round your answer to the nearest cent.)

Answer 1

Explanation:

After 5 years at a simple interest rate of 10%, Patrick would have earned $500 in interest ($1000 x 10% x 5 years). So at the end of the 5 years, he would have $1500 in the account.

If this entire amount is deposited into a new account that earns 10% compounded quarterly, we need to determine the quarterly interest rate first.

The quarterly interest rate is (1 + 0.10/4)^4 - 1 = 0.025 (rounded to three decimal places).

After 10 years (or 40 quarters) at a quarterly interest rate of 0.025, the compounded amount is:

$1500 x (1 + 0.025)^40 = $4045.56

Therefore, Patrick would have $4045.56 in the account after 10 years when rounding to the nearest cent.

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