Question

Lou has an account with $10,000 which pays 6% interest compounded annually. if to that account, lou deposits $5,000 at the beginning of each year for 2 years, find out the amount in the account after the last deposit.

Answer 1

ince the problem is only asking for 4 years, we can just calculated it out year by year. Recall the formula for compounding interest: A = P(1+r)n, where A is the total amount, P is the principle (amount you start with), r is the interest rate per period of time, and n is the number of periods (in this case, r is annual interest rate, so n is number of years). At the beginning (Year 0), Lou starts off with 10000: A = 10000 At the end of Year 1, Lou earned interest on that amount, plus he has deposited another 5000: A = 10000(1.08) + 5000 End of Year 2, Lou's interest from the year 0 amount has compounded, he has started earning interest on the amount deposited last year, and he deposits another 5000: A = 10000(1.08)2 + 5000(1.08) + 5000 End of Year 3, same idea. Lou has earned compounding interest on all existing deposits, and deposits another 5000: A = 10000(1.08)3 + 5000(1.08)2 + 5000(1.08) + 5000 End of Year 4, same idea: A = 10000(1.08)4 + 5000(1.08)3 + 5000(1.08)2 + 5000(1.08) + 5000 = 36135.45