Astate lotto has a prize that pays $900 each week for 25 years.
find the total value of the prize
if the state can earn 9% interest on investments, how much money will they need to put into an account now to cover the weekly prize payments?

The total amount paid over 25 years is $1170000 ;

To cover for the amount paid, the company has to deposit $360,000 in an account which gives an interest of 9% per annum.

Amount paid per week = $900

Number of years = 25 years

Total amount paid = (Amount paid per week × number of weeks)

Number of weeks in 25 years :

Recall :

1 year = 52 weeks

25 years = (25 × 52) = 1300 weeks

Total amount paid for 25 years :

($900 × 1300) = $1,170,000

B.)

Using the simple interest formula : A = P(1 + rt)

A = total amount earned = 1170000

Let :

Principal = P

Interest rate, r = 9%

Time, t = 25 years

A = P(1 + (0.09 × 25))

1170000 = P(1 + 2.25)

1170000 = P(3.25)

1170000 / 3.25 = P

P = $360,000

Hence, the company will need to put in $360,000 to cover the weekly price payment.

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Givens

To find the total amount of money that this prize pays, we need to find the total number of weeks that represents 25 years, and then multiply that number with $900.

So, we know that 1 year has 52 weeks, so 52 weeks multiplied by 25 years is

This means there are 1300 weeks, and the prize pays $900 to each of them, so

Therefore, after 25 years, the prize will pay $1,170,000.

Now, if the state can earn 9% interest, the total interest amount would be

In this case, the principal must be the difference between $1,170,000, and the interest earned, as follows

The interest earned is $810,000. Now, the principal is

Therefore, the need to put into an account $360,000 to cover weekly prize payments.

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80 the answer is 80

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