Question

An annuity immediate pays$1000 at the end of the first year. The payment increases by 3% per year to compensate for inflation. What is the present value of this annuity on the basis of a rate of 7%, if it runs for 20 years?

Answer 1

solution

$Payment, P=1000$

$Growth\ rate, g=0.03$

$Interest,r=0.07$

$Period,n=20$

$$Present\ value,PV=\frac{P}{r-g}[1-(\frac{1+g}{1+r})^n]$$

$$=\frac{1000}{0.07-0.03}[1-(\frac{1.03}{1.07})^{20}]=13331.6634$$

Answer: the present value is $13,331.66