Question

Your uncle is about to retire, and he wants to buy an annuity that will provide him with $80,000 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 him to buy the annuity today?

Answer 1

Here n = no . of years = 20 years

Annuity = 80000$

r = rate of interest = 5.25%

Since first payment is coming immediately formula of annuity due will be used

PV(annuity due) = A[1-(1/(1+r)^n / r ] x (1+r)

=80,000 x [1-(1/(1+5.25%)^20 / 5.25%] x (1+5.25%)

=80,000 x [1-(1/(1+0.0525)^20 / 0.0525] x (1+0.0525)

=80,000 x [1-(1/(1.0525)^20 / 0.0525] x (1.0525)

=80000 x [1-0.3594 / 0.0525] x 1.0525

=80000 x [0.6406/0.0525] x 1.0525

= 80000 x 12.2022 x 1.0525

= 10,27,427.14 $

Thus annuity will cost 10,27,427.14 $ today