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

$1,213,657.685

Step-by-step 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* ((1 - (1 + g)^n * (1 + i)^(-n))/(i - g)`

`= \$2,250* (((1 - (1 + 0.04)^(45)* (1 + 0.06)^(-45))/(0.06 - 0.04))\\\\ = \$2,250 * (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.