Question

Question 3 Unsaved Today is Janet’s 23rd birthday. Starting today, Janet plans to begin saving for her retirement. Her plan is to contribute $ 4 ,000 to a brokerage account each year on her birthday. Her first contribution will take place today. Her 42nd and final contribution will take place on her 64th birthday. Her aunt has decided to help Janet with her savings, which is why she gave Janet $ 2 0,000 today as a birthday present to help get her account started. Assume that the account has an expected annual return of 8 percent. How much will Janet expect to have in her account on her 65th birthday?

Answer 1

There is two part of this question.

1st part: Janet is contributing $4000 per year

So value of this amount at her 65th year will be given by following formula

= (1+r) *P * ((1+r)^n - 1)/r

where r is annual return which is 8%

n is number of years which is 42 years

P is periodic amount which is $4000

while puting all this value in equation we will get

future value = 1.08 * 4000 * (1.08^42 - 1)/.08

= $1,314,332.02

2nd part is amount given by her anut

future value of $20000 at 65th birthday = 20000 * (1.08)^42 = $506789.64

Janet expect to have $1821121.66 in her account on her 65th birthday.