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

Step-by-step explanation:

Formula: Future value of annuity =$P[\dfrac{(1+r)^n-1}{r}]$, 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= $\dfrac{0.06}{4}=0.015$  

Number of periods: n = 4x 40 =160

Now, Future value of amount when Mr. Pink turns 28 years = $1800(\dfrac{(1+0.015)^{160}-1}{0.015})$

$=1800(\dfrac{10.8284615777-1}{0.015})\\\\=1800\times\dfrac{9.8284615777}{0.015}\\\\\approx\ 1179415.39$

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