samanthamason13
Answered

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

Verified Answer :

nobillionaireNobley

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

Answer:

The correct option is b.

Step-by-step explanation:

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

The formula for ordinary annuity is

\(PV=\frac{P[1-(1+r)^{-n}]}{r}\)

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

\(PV=\frac{100000[1-(1+0.05)^{-20}]}{0.05}\)

\(PV=1246221.03425\)

\(PV\approx 1,250,000\)

Therefore the correct option is b.