Question

Q1.

An investment company offers you an annuity of $20,000 per year for the next 10 years. The interest rate is 10%. How much would you be willing to pay for the annuity?

Q2.

You have $100,000 to invest now and would also like to invest $6,000 for each of the next five years in an investment which returns 8% per year. With annual compounding, how much will your investment be worth in 5 years?

Answer 1

1.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=$20,000[1-(1.1)^-10]/0.1

=$20,000*6.144567106

=$122,891.34(Approx).

2.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
Hence future value of $100,000=$100,000*(1.08)^5

Also:

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

=$6000[(1.08)^5-1]/0.08

Hence total investment value would be

=$100,000*(1.08)^5+$6000[(1.08)^5-1]/0.08

=($100,000*1.469328077)+($6000*5.86660096)

=$182,132.41(Approx).