Debbie invests $100 in an account that pays 3% annual interest, compounded monthly. Rachel invests $80 in an account that pays 2.5% annual interest compounded weekly. Whose balance is greater after 1 year?

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The formula for compound interest is A = P(1+r)^t, where A = total amount, P = principal (initial amount), r = interest rate (in decimal form), and t = time in years. The rate is 5%. 5% is 0.05 in decimal form. 1 + 0.05 is 1.05. 1 is added, because the 1 represents the whole amount and the amount of money in the account grows. t = 10. Using a calculator, raise 1.05^10. You should get the long decimal 1.62889462678. Do not delete it from the calculator. Multiply it by 1,000 to find the new amount. You get 1,628.89462678 or 1,628.89 when rounded to the nearest hundredth. There. Rachel will have $1,628.89 in her bank account after 10 years.

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