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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 =
where P is the loan amount;
r = 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 = ; n = 2*52 = 104.
Substitute these values into the formula and get for monthly payment
M = = $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.