Answer:
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
[tex]52 \times 25 = 1300[/tex]
This means there are 1300 weeks, and the prize pays $900 to each of them, so
[tex]900 \times 1300 = 1,170,000[/tex]
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
[tex]Interest=Principal \times Rate \times Time[/tex]
In this case, the principal must be the difference between $1,170,000, and the interest earned, as follows
[tex]i=(1,170,000-i) \times 0.09 \times 25\\i= (1,170,000-i) \times 2.25\\i=2,632,500- 2.25i\\i+2.25i=2,632,500\\3.25i=2,632,500\\i=\frac{2,632,500}{3.25}\\ i=810,000[/tex]
The interest earned is $810,000. Now, the principal is
[tex]P=1,170,000-810,000=360,000[/tex]
Therefore, the need to put into an account $360,000 to cover 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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