Small investment of 3.6% interest compounded monthly.

Question

Jelena made an investment into an account that bore 3.6% compounded monthly. She let it sit for 20 years and ended up with an account balance $20,522.20 How much did she originally invest?

Answer 1

Understanding this question revolves around identifying the correct time periods and interest rates.

Since the investment compounds monthly, we first need to find the monthly interest rate. If we assume that the 3.6% is an annual interest rate, the monthly interest rate is 0.30%. That interest is compounded over 240 monthly periods (20 years * 12 months) and results in the $20,522.20 final balance in the account.

Setting up our initial equation looks like this:

$20,522.20 = C₀*(1+0.30%)²⁴⁰

C₀ = $20,522.20/1.003^240

C₀ = $10,000