John and Peter both want to save some money. John decides to save $1,000 every y

Question

John and Peter both want to save some money. John decides to save $1,000 every year in an account that pays 4% interest per year compounded annually. Peter is a little less organized and doesn’t get around to depositing money into his savings account, which also pays 4% interest per year compounded annually, until 5 years later. He thinks he’ll try and make up the time by depositing $1,400 into the account every year from then on. How much will be in each person’s account at the end of 20 years, counting from when John started saving, compared to the total amount that each person put in?

Explanation / Answer

John's Account after 20 years (Future Value) = 1000 * (F/A,4%,20 years) = 1000 * 29.778 = $29,778

(Use Future value of an annuity table to find (F/A,4%,20 years) or use excel formula = FV(4%,20,-1) = 29.778)

For Peter the annuity only starts after 5 years, i.e only for 15 years.

Peter's account after 20-5 years (Future Value) = 1400*(F/A,4%,15 years) = 1400* 20.024 = $28,033

(Use Future value of an annuity table to find (F/A,4%,15 years) or use excel formula = FV(4%,15,-1) = 20.024)

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