Question

Suppose Mr. Pink is 28 years old right now and puts away $1,800 per quarter in an account that returns 6% interest. a.) How much will be in the account when he turns 68? b.)What is his total contribution to the account?

Answer 1

Answer: (a) When he turns 68 , the account will have = $1,179,415.39

(b) $ 288,000

Explanation:

Formula: Future value of annuity =
`P[((1+r)^n-1)/(r)]`, where P+ periodic payment, r = rate of interest per period, n= number of periods.

As per given, we have

P= $1800

rate of interest = 6% = 0.06

(a) n= 68-28 = 40

Rate per period : r=
`(0.06)/(4)=0.015`

Number of periods: n = 4x 40 =160

Now, Future value of amount when Mr. Pink turns 28 years =
`1800(((1+0.015)^(160)-1)/(0.015))`

`=1800((10.8284615777-1)/(0.015))\\\\=1800*(9.8284615777)/(0.015)\\\\\approx\$1179415.39`

Hence, when he turns 68 , the account will have = $1,179,415.39

(b) Total contribution = P × n

=1800 × 160

=$ 288,000

Hence, Total contribution =$ 288,000