Question

A person who is about to retire has accumulated $100,000 in a savings account. Suppose that the person withdraws $8,195.23 from the savings account at the end of each year for 20 years, at which time the account is totally depleted. What is the interest rate, based upon annual compounding?

Answer 1

$PV=A\times\frac{1-\frac{1}{(1+r)^n}}{r}$

PV=100 000

A=8195.23

n=20

$100 000=8 195.23\times\frac{1-\frac{1}{(1+r)^{20}}}{r}$

$12.20=\frac{1-\frac{1}{(1+r)^{20}}}{r}$

$12.20=\frac{1-\frac{1}{(1+r)^{20}}}{r}$

$12.20=\frac{1}{r^{21}}$

$r^{21}=0.081952$

r=0.887697