Question

Mitch and Bill are both age 75. When Mitch was 24 years​ old, he began depositing ​$1500 per year into a savings account. He made deposits for the first 10​ years, at which point he was forced to stop making deposits.​ However, he left his money in the​ account, where it continued to earn interest for the next 41 years. Bill​ didn't start saving until he was 49 years​ old, but for the next 26 years he made annual deposits of ​$1500. Assume that both accounts earned an average annual return of 6​%​(compounded once a​ year).

a.) How much does Bill have in his account at age 75?

b.) Compare the amounts of money that Mitch and Bill deposit into their accounts. How much do Mitch and Bill deposit into thier accounts?

Answer 1

(a) If you start with 0.00 in a savings account earning a 6% interest rate, compounded Annually, and make 1,500.00 deposits on a Annual basis, after 26 Years your savings account will have grown to 89,178.25 -- of which 39,000.00 is the total of your beginning balance plus deposits, and 50,178.25 is the total interest earnings.

At the age of 75 Bill will have $89,178.25 in his account.

(b) Bill and Mitch both deposit $1500 annually but Bill deposits for 26 year and Mitch only for 10 years, so Bill's deposits are more than Mitch.

Mitch's total deposit = $1500 × 10 = $15000

Bill's total deposit = $1500 × 26 = $39000