05-11-2007, 04:51 PM
OK....anybody that knows how to use this calculator, please chime in on this, cuz I can't seem to figure out how to compute this problem on my calculator (the $200K option over 5 years). Please advise.
A man wins a sweepstakes giving away one million dollars. He has two options for receiving the money; he can either take two hundred thousand dollars a year for five years or $747,300 now. With a discount rate of 6%, which option has the higher present value?
A) $747,300 now
B) Annual payments of $200,000 for 5 years
C) The present value cannot be computed from the information given
D) Both have equal present values
Detailed Explanation:
Annual payments of $200,000 for 5 years.
$842,472.76 = 200000[(1/.06) - (1/(.06(1.06^5)))]
Present Value = Annual Fixed Payments[(1/interest rate) - (1/(interest rate((1+interest rate)^number of years)))]
To find the present value of the $200,000 annual payments for 5 years, we must plug it in the equation above. We plug in the discount rate in place of the interest rate, and we get the answer $842,472.76. When this is compared to $747,300, which is the present value of one million dollars in 5 years at a 6% discount rate, the annual payments have a higher present value.
Another option to solve this problem, is to use the âpresent value of an annuityâ table. Multiply $200,000 with 4.2124, which we get when we look for 6% and 5 years, and we get $842,480. This is not an exact answer, but it is close enough to determine that the present value of the annual payments is considerably higher than the one-time payment.
A man wins a sweepstakes giving away one million dollars. He has two options for receiving the money; he can either take two hundred thousand dollars a year for five years or $747,300 now. With a discount rate of 6%, which option has the higher present value?
A) $747,300 now
B) Annual payments of $200,000 for 5 years
C) The present value cannot be computed from the information given
D) Both have equal present values
Detailed Explanation:
Annual payments of $200,000 for 5 years.
$842,472.76 = 200000[(1/.06) - (1/(.06(1.06^5)))]
Present Value = Annual Fixed Payments[(1/interest rate) - (1/(interest rate((1+interest rate)^number of years)))]
To find the present value of the $200,000 annual payments for 5 years, we must plug it in the equation above. We plug in the discount rate in place of the interest rate, and we get the answer $842,472.76. When this is compared to $747,300, which is the present value of one million dollars in 5 years at a 6% discount rate, the annual payments have a higher present value.
Another option to solve this problem, is to use the âpresent value of an annuityâ table. Multiply $200,000 with 4.2124, which we get when we look for 6% and 5 years, and we get $842,480. This is not an exact answer, but it is close enough to determine that the present value of the annual payments is considerably higher than the one-time payment.
Matymus Primehilarious Waterloo, NY
Excelsior College
B.S. General Business, Class of 2008
Fall 2011 - currently pursuing Pre-Pharmacy
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