Question

Alecia deposited $500 in a savings account at 5% compounded semiannually. What is her balance after 6 years?

Answer 1

Hello! The formula for compound interest is P ( 1 + r/n)^nt, where P = principal, r = percentage rate, n = times compounded per year, t = amount of time in years. This can be confusing, so let's take it step-by-step. 5% is the rate. 5% in decimal form is 0.05. Semi-annually means every 6 months. In other words, this is compounded 2 times a year. 0.05/2 is 0.025. 1 + 0.025 is 1.025. We're looking for the amount over 6 years. Now, we multiply n and t together. 2 * 6 = 12. The amount will be compounded 12 times over 6 years, so we raise the decimal to the 12th power. 1.025^12 is 1.34488882425, but don't delete that decimal from your calculator. Now, multiply that decimal by 500. When you do, you get 672.444412123 or 672.44 when rounded to the nearest hundredth. There. Alecia's balance after 6 years is $672.44.