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 “present value of an annuity” 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 Prime
Lincoln, NE
Excelsior College
B.S. General Business


~105 Credits down - 15 to go~

This is the response i got from my sis who used to work in finance. I dont know if its right though or answers your question.

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Net present value - Wikipedia, the free encyclopedia

yeah i know how to calculate it, but it takes a while...not as simple as it looks. here is the formula...U try! hahahaha.......and the answer would be to take payments of $200,000 for 5 years because the interest will compound over time. if you took the lump sum the value of the money would be as is today and over 1yr. you would only receive approx. $792,138 dollars vs. $1,338,225.60 over the next 5 years as the interest compounds.
so there.