Question

2. 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 the year, she invests the accumulated savings ($1,095) in a brokerage account with an expected annual return of 12%. a) How much money will she save when she turns 65 years old? b) If she does not start saving until she is 40 years old, how much will she have by age 65?

Answer 1

Solution -2:

A 20 Year old student wants to save $3 per day for a year for retirement

At the end of the 21st year, she invests total saving of $1095 in brokerage account

Expected annual return = 12%

(a)How much money will she save when she turns 65 years old?

In this case we have to calculate Future Value of single cash flow

Future value of single Cash Flow = A x (1 +i) ⁿ

Here, A = Amount of investment = $1,095

i = Interest Rate = 12%

n = Number of years = 45 years ( 65 years - 20 years )

Putting these values in the formula

= 1,095 x ( 1 + 0.12) ⁴⁵

= 1,095 x ( 1.12) ⁴⁵

= 1,095 x 163.98746

= 179566.426

= $179,566

(b)If she does not start saving until she is 40 years old, how much will she have by age 65:

In this case the number of years will be = 65 years - 40 years = 25 years

Interest rate = 12%

Annuity per day ( investment) = $1,095

Future Value of single cash flow = A x (1 + i) ⁿ  

= 1,095 x ( 1 + 0.12 ) ²⁵

= 1,095 x ( 1.12) ²⁵

= 1,095 x 17

= $18,615