Question

Ed and Edna are both medical doctors and have just finished paying off their medical school loans. Ready to get serious about saving for retirement, they want to set aside funds from their practices at the end of each year so that their retirement fund will be $10 million in 30 years. They assume an average portfolio return of 6.5% before they retire, a 4.5% average return after they retire, and a 2.5% average inflation rate. They want to plan for a retirement lasting 35 years. How much will they need to save each year? 

A. $80,620. B. $108,710. C. $115,775. D. $88,560. E. $86,400.

Answer 1

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

In Problem, it doesn't specify the funds at retirement is Real terms. Hence inflation is ignored.

Particulars	Amount
FV of Annuity	$ 10,000,000.00
Int Rate	6.5000%
Periods	30

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$10000000 = Cash Flow * [ [ ( 1 + 0.065 ) ^ 30 ] - 1 ] / 0.065
$10000000 = Cash Flow * [ [ ( 1.065 ) ^ 30 ] - 1 ] / 0.065
$10000000 = Cash Flow * [ [ ( 6.6144 ] - 1 ] / 0.065
$10000000 = Cash Flow * [ 5.6144 ] / 0.065
Cash Flow = $ 10000000 * 0.065 / 5.6144
Cash Flow = $ 115774.42

Annual Contribution required is $ 115775

Option C is correct.