SOLUTION: Jessica borrowed $5000 from the bank in order to buy a new piano. She will pay it off by equal payments at the end of 2 years. The interest rate is 8% compounded weekly. Determine

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Question 1206629: Jessica borrowed $5000 from the bank in order to buy a new piano. She will pay it off by equal payments at the end of 2 years. The interest rate is 8% compounded weekly. Determine the size of the payments and the total interest paid
Answer by ikleyn(52787) About Me  (Show Source):
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Jessica borrowed $5000 from the bank in order to buy a new piano.
She will pay it off by equal payments at the end of 2 years.
The interest rate is 8% compounded weekly.
Determine the size of the payments and the total interest paid
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Use the formula for the periodical payment for a loan

    M = P%2A%28r%2F%281-%281%2Br%29%5E%28-n%29%29%29


where P is the loan amount; 

r = 0.08%2F52 is the effective interest rate per period (per week in this problem);

n is the number of payments (total number of weeks in this problem); 

M is the payment for the period (weekly payment in this problem).



    In this problem  P = $5000;  r = 0.08%2F52;  n = 2*52 = 104.



Substitute these values into the formula and get for monthly payment

    M = 5000%2A%28%28%280.08%2F52%29%29%2F%281-%281%2B0.08%2F52%29%5E%28-104%29%29%29 = $52.07.


Thus, the weekly payment is $52.07.


In total, Jane will have to repay  2*52*52.07 = 5415.28 dollars in 2 years.


The difference $5,415.28 - $5,000 = $415.28  is the interest she will pay for this loan.

Solved.