Johnny wishes to borrow €10,000 at 12% per annum compounded monthly. What equal monthly payments, to the nearest whole euro, would Johnny need to make amortise the loan over 5 years? €206 €120 €294 €187€222
Question
Johnny wishes to borrow €10,000 at 12% per annum compounded monthly. What equal monthly payments, to the nearest whole euro, would Johnny need to make amortise the loan over 5 years? €206 €120 €294 €187€222
Solution
To solve this problem, we need to use the formula for the monthly payment on an amortizing loan, which is:
P = [r*PV] / [1 - (1 + r)^-n]
where: P = monthly payment r = monthly interest rate (annual rate / 12) PV = present value, i.e., the amount of the loan n = total number of payments (months)
Given in the problem: PV = €10,000 annual interest rate = 12% = 0.12 (in decimal form) r = 0.12 / 12 = 0.01 n = 5 years * 12 months/year = 60 months
Substituting these values into the formula:
P = [0.01*10000] / [1 - (1 + 0.01)^-60]
Calculating the above expression will give us the monthly payment Johnny needs to make to amortize the loan over 5 years.
After calculating, we find that P = €222.44. Rounding to the nearest whole euro, Johnny would need to make monthly payments of €222.
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