Question

5. You want to retire in ten years and you currently have no wealth to your name. You estimate that you’ll will need $1.8M at your retirement date in order to live out the remainder of your life comfortably. You plan to make 10 equal annual payments into an account at the end of each year from now until your retire. If you can earn 8%/year, compounded annually, how much must you invest at the end of each year for the next 10 years?

Answer 1

Sol:

Future value (FV) = $1.8 million

Interest rate = 8% per year

Periods (NPER) = 10 years

To determine how much amount you invest at the end of each year for the next 10 years we can use PMT function in excel:

FV	1,800,000
Interest rate	8%
NPER	10
Annual Payment	$124,253.08

Therefore the amount you invest at the end of each year for the next 10 years to achieve your goal will be $124,253.08

Workings

Also to determine how much amount you invest at the end of each year for the next 10 years you can use the below formula:

r = 8%

n = 10 years

Future value of annuity = P x (1+r)^n-1/r

1,800,000 = P x (1 + 8%)^10 - 1 / 8%

1,800,000 = P x (1.08)^10 - 1 / 0.08

1,800,000 = P x (2.1589 -1) / 0.08

1,800,000 = P x (1.1589 / 0.08)

1,800,000 = P x 14.4866

P = 1,800,000 / 14.4866 = $124,253.08