Question

Beth has recently made her last medical school loan payment. Now she wants to set aside funds at the end of each year for retirement. Right now, she has a retirement fund goal of $7 million and she wants her savings contributions to grow with inflation over time. She wants to retire in 30 years and she wants to plan for a retirement lasting 25 years. If she assumes an average portfolio return of 6.5% before retirement, a 4.5% average return after retirement, and a 2.5% average inflation rate, what is the amount of her initial contribution?

• A. $126,860.

• B. $81,040.

• C. $61,990.

• D. $76,100.

• E. $60,480.

Answer 1

Real rate of Ret from Investment = [ [ 1 + Nominal Ret ] / [ 1 + Inflation Rate ] ] - 1

Particulars	Values
Nominal rate	6.50%
Inflation rate	2.50%

Real rate = [ [ 1 + Nominal Rate ] / [ 1 + Inflation rate ] ] - 1
= [ [ 1 + 0.07 ] / [ 1 + 0.03 ] ] - 1
= [ [ 1.065 ] / [ 1.025 ] ] - 1
= [ 1.039 ] - 1
= 0.039
i.e, Real rate is 3.9 %

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

Particulars	Amount
FV of Annuity	$   7,000,000.00
Int Rate	3.9024%
Periods	30

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
$7000000 = Cash Flow * [ [ ( 1 + 0.039 ) ^ 30 ] - 1 ] / 0.039
$7000000 = Cash Flow * [ [ ( 1.039 ) ^ 30 ] - 1 ] / 0.039
$7000000 = Cash Flow * [ [ ( 3.1534 ] - 1 ] / 0.039
$7000000 = Cash Flow * [ 2.1534 ] / 0.039
Cash Flow = $ 7000000 * 0.039 / 2.1534
Cash Flow = $ 126858.45

Annual deposit required is $ 126860.

Option A is correct. DIfference is due to rounding off prolem.