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).**

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