Question

When you finally retire, you want to be able to draw from an account an annual salary of $100,000 for 20 years. Approximately how much should be in your account that has an APR of 5% when you retire, such that you can draw an annual salary of $100,000? Assume an ordinary annuity.

a.
$62,000
c.
$1,310,000
b.
$1,250,000
d.
$3,000,000

Answer 1

The correct option is b.

Explanation:

Given information:APR= 5%, Period = 20 years, Annual salary = $100,000.

The formula for ordinary annuity is

`PV=(P[1-(1+r)^(-n)])/(r)`

Where, P is periodic payment, r is rate per period and n is number of periods.

`PV=(100000[1-(1+0.05)^(-20)])/(0.05)`

`PV=1246221.03425`

`PV\approx 1,250,000`

Therefore the correct option is b.

Answer 2

PV = P(1 - (1 + r)^-n) / r; where P is the periodic withdrawal = $100,000; r = rate = 5% = 0.05; n = number of periods = 20 years.

PV = 100000(1 - (1 + 0.05)^-20) / 0.05 = 100000(1 - 1.05^-20) / 0.05 = 100000(1 - 0.3769) / 0.05 = 100000(0.6231) / 0.05 = 100000(12.4622) = 1,246,221 ≈ $1,250,000