Bill starts a retirement fund at age 21 and plans on depositing equal

Bill starts a retirement fund at age 21 and plans on depositing equal annual amounts on each birthday, starting
at age 21, and ending at age 60. He wants to have $2 million at age 60. John starts his fund on his 30th birthday.

He wants to deposit equal annual amounts on each birthday starting on his 30th birthday and ending on his
60th birthday. John wants to have $2 million at age 60. If the investment funds earn 10% per year, calculate the
amounts the Bill and John respectively will have to save each year (rounded to the nearest dollar) to meet their
goals. Comment on the difference.

ANSWER

Bill will need to make deposits of $4,519 per year, while John will need to make deposits of $10,992 per year. These
amounts are based on the future value of the annuity in each case of $2,000,000, N = 40 for Bill and N = 31 for John,
with I = 10%. The difference illustrates the importance of compounding and the need to begin saving early. John’s
annual deposits are more than twice Bill’s deposits, even though the number of years is only 9 fewer, or less than 25%
less.