Question

In: Finance

How long will it take to pay off a loan of ​$52,000 at an annual rate...

How long will it take to pay off a loan of ​$52,000 at an annual rate of 12 percent compounded monthly if you make monthly payments of ​$750​? Use five decimal places for the monthly percentage rate in your calculations.

The number of years it takes to pay off the loan is ____ years. (Round to one decimal​ place.)

Solutions

Expert Solution

Solution:
Calculation of equal annual installement
Loan Amount(P) $ 52,000.00
Annual rate of interest (i) 12% pa compunded monthly
0.01
EMI = $750.00
P = R[1-(1+i)^-N]/i
52000 = 750[1-(1+0.01)^-N]/0.01
52000*0.01/750 = 1-(1.01)^-N
                                                                                                 0.6933 = 1-(1.01)^-N
1.01^-N = 0.3067
Taking Log both side
-N Log1.01 Log 0.3067
-N Log 0.3067/log 1.01
-N -118.78
N 119 Months
or 9 Years 11 Months

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