Question

A 20-year-old student wants to save $5 a day for her retirement. Every day she places $5 in a drawer. At the end of each year, she invests the accumulated savings ($1,825) in a brokerage account with an expected annual return of 8%. If she keeps saving in this manner, how much will she have accumulated at age 65? If a 40-year-old investor began saving in this manner, how much would he have at age 65? 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?

Answer 1

Answer:

Instructions are listed below

Explanation:

Giving the following information:

At the end of each year, she invests the accumulated savings ($1,825) in a brokerage account with an expected annual return of 8%. She will invest for 45 years.

A) We need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

FV= {1825[(1.08^45)-1]}/0.08= $705,372.75

B) n= 25

FV= {1825[(1.08^25)-1]}/0.08= $133,418.34

C) FV= 705,372.75     A=?

We need to isolate A:

A= (FV*i)/{[(1+i)^n]-1}

A=(705,372.75*0.08)/[(1.08^25)-1]

A= $9,648.64