You just won the lottery, which will pay you $1,000 a year until you pay it off.

Question

You just won the lottery, which will pay you $1,000 a year until you pay it off. The current interest rate is 5%. The first payment happens in 1 year. a) As we know the lottery will pay 10 times, what is this lottery actually worth today? b) Forget about what you got in part a), if you know the prize is worth $10,000, and you will still receive $1000 a year until the prize is paid off. The interest rate is still 5%. How long does it take for you to be paid off? c) It turns out the prize would pay you $1000 a year forever. For the first 4 years, the interest rate is 5%, then the rate falls into 4% for the next 3 years, then goes up to 6% forever. What is your prize worth today?

Explanation / Answer

a)

n=10
rate =0.05
pmt=1000
Using excel PV function:
=PV(0.05,10,1000)
=$7,721.73

b)Here:
PV=10,000
pmt=1000
rate =0.05
Using excel nper function:
=NPER(0.05,1000,-10000)
=14.21 years

c) Value at the end of 7 years i.e. when the 6% period begins = 1000/0.06=$16,666.67
Discounting it back by 4% for 3 years:
=16,666.67/(1.04^3)=$14,816.61
Discounting it back by 5% for 4 years:
=14,816.61/(1.05^4)=$12,189.66

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