Question 1206629
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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*(r/(1-(1+r)^(-n)))}}}


where P is the loan amount; 

r = {{{0.08/52}}} 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 = {{{0.08/52}}};  n = 2*52 = 104.



Substitute these values into the formula and get for monthly payment

    M = {{{5000*(((0.08/52))/(1-(1+0.08/52)^(-104)))}}} = $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.
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Solved.