A 20-year-old student wants to save $3 a day for her retirement. Every

QUESTION

A 20-year-old student wants to save $3 a day for her retirement. Every day she places $3 in a drawer. At the end of each year, she
invests the accumulated savings ($1,095) in a brokerage account with an expected annual return of 12%.
(1) If she keeps saving in this manner, how much will she have accumulated at age 65?
(2) If a 40-year-old investor began saving in this manner, how much would he have at age 65?
(3) How much would the 40-year-old investor have to save each year to accumulate the same amount at 65 as the 20-year-old investor?
1. If the savings are accumulated and invested at the end of every year from 20th year to 65th year, we have an ordinary annuity for 45 years. If savings of $1095 are invested at the end of every year for 45 years, then the student will have an accumulated balance of $1,487,261.89 at her 65 year. 2. If the savings are accumulated and invested at the end of every year from 40th year to 65th year, we have an ordinary annuity for 25 years. If savings¦

f $1095 are invested at the end of every year for 25 years, then the investor will have an accumulated balance of $146,000.59 at her 65 year. 3. To accumulate the same amount at the end of 65th year as the 20-year old student, the 40-year old investor needs to invest $11,154.42 each year for 25 years.

ANSWER:

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