Question

1. You have won the lottery and will receive $20,000 each year for the next 20 years! A financial services company has offered you an upfront payment of $200,000 for the entire income stream. If you estimate the time value of money for you is 5%, would you accept the offer? Explain.

2. A family spends $45,000 on living expenses. If inflation averages 3% over the next 5 years, how much would the family need to spend after 5 years to maintain their standard of living?

Answer 1

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

=20,000[1-(1.05)^-20]/0.05

=20,000*12.4622103

=$249,244.21(Approx)

Hence offer should not be accepted as it has a lower present value as compared to $20,000 received each year for 20 years

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.

A=45000*(1.03)^5

=45000*1.15927407

=$52167.33(Approx)