SOLUTION: A state lotto has a prize that pays $1,300 each week for 25 years. Find the total value of the prize: $ If the state can earn 4% interest on investments, how much money

Question 1137941: A state lotto has a prize that pays $1,300 each week for 25 years.
Find the total value of the prize: $

If the state can earn 4% interest on investments, how much money will they need to put into an account now to cover the weekly prize payments?
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
A state lotto has a prize that pays $1,300 each week for 25 years.
Find the total value of the prize.

DISCLAIMER:
First, you have to find how many weeks there are in 25 years. The easy answer to this is 1300 weeks, since 52 weeks in a year multiplied by 25 years is 1300 weeks. However, this is slightly inaccurate since 52 weeks is only 364 days. (A year is either 365 or 366 days.) 365 days multiplied by 25 years is 9125 days. Over a 25-year period, there will also be either six or seven leap days, upping the total number of days over 25 years to either 9131 or 9132. Divide this by 7, and it comes to 1304 weeks and 3 days (or 1304 weeks and 4 days), a full 4.5 weeks more than 1300 (if you were to simply multiply 25 by 52.)

This all being said, I'm going to assume they simply want you to multiply 25 by 52 to come out with a "clean" number of 1300 weeks.

1300 weeks multiplied by $1300 is $1,690,000. So, that's the total value of the prize.

If the state can earn 4% interest on investments, how much money will they need to put into an account now to cover the weekly prize payments?

If you use the simple interest formula:
Interest = Principal * Rate * Time

i = (1690000 - i) * 0.04 * 25

i = (1690000 - i) * 1

i = 1690000 - i

2i = 1690000

i = 845000

This means the interest earned will be $845,000. We know that the principal is: 1690000 - i. Substituting i = 845000, this means the principal is also $845,000.

So, $845,000 needs to be put into an account now at 4% annual interest to accrue $845,000 interest, for a grand total of $1,690,000 at the end of 25 years.

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