Question

Because your mother is about to retire, she wants to buy an annuity that will provide her with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost her to buy the annuity today

Answer 1

The calculated present value of the annuity is $915,166.70.

Explanation and Solution:

Annuity is a collection of fixed payments made or earned either at the close or at the beginning of any term such that a significant initial payment or receipt may be turned into a set of comparatively minor payments or receipts. An annuity that lasts indefinitely is called perpetuity.

The formula for the present value of the annuity is given by:

$P = \frac{1- (1+i)^{-n} }{i} * R$

Where;

R = annual payment = $75,000

i = interest rate = 5.25%

P = Present value of annuity

n = number of years = 20 years

P = $\frac{1- (1+5.25)^{-20} }{5.25} * 75,000$

P = $915,166.70