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%. (1) If she keeps saving in this manner, how much will she have accumulated at age 65

Answer 1

Answer:

$147,425

Explanation:

Step 1: If a student saves $5 a day for a year, she then has

$5 × 365 days = $1,825

N.b: 365 days makes a year

Step 2: If she invests the yearly savings in a brokerage account that has an expected return of 8%, at the end of a year she would have

$1,825 + (8% of $1,825) at the end of the year.

solving the above, we have

$1,825 + (0.8 × $1,825)

$1,825 + $1,460 = $3,285

At the end of every year after investment, she has $3,285

Step 3: At te age of 65(which is 45 years later; i.e 65years - 20years), she would have saved up

$3,285 × 45 years = $147, 825

At the age of 65, she would have saved up $147,825.