Question

Bert and Bertha estimate when they retire in 18 years that their retirement portfolio will need to have a value of $2,000,000 to finance their desired retirement lifestyle. They believe inflation will average 2% over time and their retirement investment return will average 8% until they retire. After they retire, they will invest more conservatively and the portfolio will average a 5% return during a 25 year retirement. If they currently have nothing saved for retirement, how much will they need to save at the end of each year to meet their retirement goal

Answer 1

Answer:

$46733.10

Explanation:

If Bert and Bertha currently have nothing saved for retirement, they need to save $46733.10 at the end of each year to meet their retirement goal.

DATA

r = Periodic Interest rate = 8%

g = Inflation rate = 2%

n= no of periods = 18

C= Periodic Payments

FV of growing annuity = 2,000,000

Solution

$FV of growing annuity =C * \frac{((1+r)^n - (1+g)^n)}{r-g}$

2,000,000 = C  ((1+0.08)^17) - (1+0.02)^18)) / 0.08 - 0.02

2,000,000 = C  (3.99601949918 - 1.42824624758) / 0.06

120,000 =  C (2.5677732516)

C = $46733.10