Question

Problem 4 and 5-1 Future Value

Consider that you are 35 years old and have just changed to a new job. You have $83,000 in the retirement plan from your former employer. You can roll that money into the retirement plan of the new employer. You will also contribute $3,900 each year into your new employer’s plan.

  

If the rolled-over money and the new contributions both earn a 7 percent return, how much should you expect to have when you retire in 30 years? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

  

Future value

$

Answer 1

Step 1
Calculation of future value of rolled over money i.e. $83000
We can use the Future value of sum formula.
FV = P * (1+r)^n
FV = Future value of rolled over money = ?
P = Rolled over money = $83000
r = rate of interest per year = 7%
n = no.of years = 30
FV = 83000 * (1+0.07)^30
Future value of rolled over money = $6,31,817.17
Step 2
Calculation of future value of yearly contribution of $3900
We can use the Future value of annuity formula.
FV of annuity = P*{[(1+r)^n -1]/r}
FV of annuity = future value of yearly contribution = ?
P = Yearly contribution = $3900
r = rate of interest per year = 7%
n = no.of years = 30
FV of annuity = 3900*{[(1+0.07)^30 -1]/0.07}
FV of annuity = 3900*94.46079
FV of annuity = 368397.07
Future value of yearly contribution = $3,68,397.07
Amount in retirement fund = $631817.17 + $368397.07 = $10,00,214.24
When you retire in 30 years , you expect to have $10,00,214.24