Assume that you just won the state lottery. Your prize can be taken either in the for of $40,000 at the end of each of the next twenty-five years (i.e. $1 million over twenty-five years) or as lump sum of $500,000 paid immediately.
a. If you expect to be able to earn 5% annually on your investments over the next twenty-five years, which alternative should you take? Why?
b. Would your decision in part (a) be altered if you could earn 7% rather than 5% on your investments overthe twenty-five years? Why?
c. At approximately what interest rate would you be indifferent when choosing between the two plans?
Solution
a. FV= PV ( 1+r)^ n
Alternative 1
= 40,000 ( 1+ .05)^25 + 40,000 ( 1+ .05)^24 + 40,000 ( 1+.05)^23 + 40,000 (1+.05)^22 + 40,000 (1+.05)^21 + 40,000 (1+.05)^20 + + 40,000 (1+.05)^19 + 40,000 (1+.05)^18+ 40,000 (1+.05)^17+ 40,000 (1+.05)^16+ 40,000 (1+.05)^15 + 40,000(1+.05)^ 14 + 40,000 (1+.05)^13+ 40,000 (1+.05)^12 + 40,000(1+.05) ^11 + 40,000(1+.05)^10 + 40,000 (1+.05)^9 + 40,000 ( 1+.05)^8 + 40,000 (1+ .05)^ 7 + 40,000 (1+.05)^6 + 40,000 (1+.05)^5 + 40,000 (1+.05)^4 + 40,000 (1+.05)^3 + 40,000 (1+.05)^2 + 40,000 (1+.05)
= 135,454.20 + 129,004 + 122,860.95 + 117,010.43 + 111,438.50 + 106,131.91 + 101,078 + 96,264.77 + 91,680.73 + 87,314.98 + 83,157.13 + 79,197.26 + 75,425.96 + 71,834.25 + 68,413.57 + 65,155.78 + 62,053.13 + 59,098.22 + 56,284.02 + 53,603.82 + 51,051.26 + 48,620.25 + 46305 + 44,100 + 42,000
= $ 2,004,537.12
Alternative 2
FOR $500,000
FV= 500,000 (1+.05)^25 = $ 1,693,177.47
Alternative 1 of $ 40,000 every year should be chosen as its future value is more than alternatuve 2.
b. same as above , it is to be calculated and on the basis of it, whose future value is more should be chosen.
c. At the interest rate where the future value of alternative 2 is more than alternative 1 it would be chosen.
Approximately 15 % interest rate.
.
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Assume that you just won the state lottery- Your prize can be taken ei.docx
1. Assume that you just won the state lottery. Your prize can be taken either in the for of $40,000 at
the end of each of the next twenty-five years (i.e. $1 million over twenty-five years) or as lump
sum of $500,000 paid immediately.
a. If you expect to be able to earn 5% annually on your investments over the next twenty-five
years, which alternative should you take? Why?
b. Would your decision in part (a) be altered if you could earn 7% rather than 5% on your
investments overthe twenty-five years? Why?
c. At approximately what interest rate would you be indifferent when choosing between the two
plans?
Solution
a. FV= PV ( 1+r)^ n
Alternative 1
= 40,000 ( 1+ .05)^25 + 40,000 ( 1+ .05)^24 + 40,000 ( 1+.05)^23 + 40,000 (1+.05)^22 + 40,000
(1+.05)^21 + 40,000 (1+.05)^20 + + 40,000 (1+.05)^19 + 40,000 (1+.05)^18+ 40,000
(1+.05)^17+ 40,000 (1+.05)^16+ 40,000 (1+.05)^15 + 40,000(1+.05)^ 14 + 40,000 (1+.05)^13+
40,000 (1+.05)^12 + 40,000(1+.05) ^11 + 40,000(1+.05)^10 + 40,000 (1+.05)^9 + 40,000 (
1+.05)^8 + 40,000 (1+ .05)^ 7 + 40,000 (1+.05)^6 + 40,000 (1+.05)^5 + 40,000 (1+.05)^4 +
40,000 (1+.05)^3 + 40,000 (1+.05)^2 + 40,000 (1+.05)
= 135,454.20 + 129,004 + 122,860.95 + 117,010.43 + 111,438.50 + 106,131.91 + 101,078 +
96,264.77 + 91,680.73 + 87,314.98 + 83,157.13 + 79,197.26 + 75,425.96 + 71,834.25 +
68,413.57 + 65,155.78 + 62,053.13 + 59,098.22 + 56,284.02 + 53,603.82 + 51,051.26 +
48,620.25 + 46305 + 44,100 + 42,000
= $ 2,004,537.12
Alternative 2
FOR $500,000
2. FV= 500,000 (1+.05)^25 = $ 1,693,177.47
Alternative 1 of $ 40,000 every year should be chosen as its future value is more than alternatuve
2.
b. same as above , it is to be calculated and on the basis of it, whose future value is more should
be chosen.
c. At the interest rate where the future value of alternative 2 is more than alternative 1 it would
be chosen.
Approximately 15 % interest rate.
