Question

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.)

Answer 1

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