Question

Farrell wants to retire in six years. To have sufficient assets to fund retirement, Farrell needs to accumulate an additional $400,000 between today and retirement. As his planner, you assume that inflation will average 5 percent. You are also confident that you can build a portfolio that will generate an 8 percent compounded annual after-tax return. What serial payment should Farrell invest at the end of the first year to fund this goal?

Answer 1

$73,070.5

Step-by-step explanation:

Inflation erodes the value of money. It makes more quantity of money to required to buy the same basket of food and services in the future.

With inflation, to calculate the the quantity of Dollars needed in n years time, we use the formula;

Inflated amount = h × (1 + f)^n

h= amount required today, f - inflation rate, n- number of years

So if Farrell needs $400,000 in 6 years time in real terms, with an inflation of 5% per year, he would need to have a quantity of money equal to

1.05^6 × 400,000 = $536,038.3.

To provide for $536,038.3 in 6 years time, he would need to contribute into a sinking fund on a yearly basis, an equal amount denoted as "A" in the formula below:

FV = A × ((1+r)^n - 1)/r

FV - 536,038.3, r - 8%, n = 6

536,038.3 = A × ((1+0.08 )^(6) - 1)/0.08)

536, 038.3 = A × 7.3359

536,038.3/7.3359 = A

$73,070.5 = A

Farrell should invest at the end of every year

$73,070.5