Question

Amy​ Parker, a​ 22-year-old and newly hired marine​ biologist, is quick to admit that she does not plan to keep close tabs on how her​ 401(k) retirement plan will grow with time. This sort of thing does not really interest her.​ Amy's contribution, plus that of her​ employer, amounts to ​$2,250 per year starting at age 23. Amy expects this amount to increase by 4​% each year until she retires at the age of 67 ​(there will be 45 EOY​ payments). What is the compounded future value of​ Amy's 401(k) plan if it earns 6​% per​ year?

Answer 1

Answer:

$1,213,657.685

Explanation:

For computation of compounded future value first we need to find out the present worth which is shown below:-

$Present\ worth = Initial\ amount\ of\ investment\times \frac{(1 - (1 + g)^n \times (1 + i)^{-n}}{i - g}$

$= \ 2,250\times (\frac{(1 - (1 + 0.04)^{45}\times (1 + 0.06)^{-45}}{0.06 - 0.04})\\\\ = \ 2,250 \times \frac{1-0.216245988}{0.02}$

= $88,172.32636

Now, Future value = Present worth × (1 + interest rate)^number of years

= $88,172.32636  × (1 + 6%)^45

= $1,213,657.685

Therefore we have applied the above formula to determine the future value.