1.You just won the $45 million lottery. You will receive $2.5 million a year for
ID: 2801023 • Letter: 1
Question
1.You just won the $45 million lottery. You will receive $2.5 million a year for the next 15 years plus an additional payment of $7.5 million at the end of 15 years. The interest rate is 11 percent.
How much is your lottery prize worth today? (Enter your answer as a positive number rounded to 2 decimal places.
2.At an interest rate of 11 percent annually, how long will it take for a $1,000 to double? To triple? (Round your answers to 2 decimal places.)
3.If you owe $50,000 payable at the end of six years, what amount should your creditor accept in payment immediately if the interest rate on the loan is 12 percent? (Enter your answer as a positive number rounded to 2 decimal places.)
Explanation / Answer
1) Present value of lottery prize =
Annuity payments*PVAF(11%, 15) + Final payment*PVF(11%, 15)
$2.5 million *7.19087 + $7.5 million*0.20900
= 17.977 million + $1.5675 million
= $19.5445 million
NOTE: The present value factors are taken from present value table. They can also be calculated using a calculator.
2) We have Future value = Present value*(1+r)n
$2000= $1000*(1+0.11)n
(1.11)n = 2
By trial and error, n= 6.64 years
SImilarly
$3000 = $1000*(1+0.11)n
(1.11)n = 3
n = 10.53 years
3) Present value of future cashflow = Future cashflow/(1+r)n
= $50000/(1+0.12)6
= $50000/1.973823
= $25331.56
So, the creditor may accept $25331.56 today which equals $50000 payable in 6 years
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