Question

How long will it take to pay off a loan of $52,000 at an annual rate of 8% compounded monthly if you make monthly payments of ​$750​? Use five decimal places for the monthly percentage rate in your calculations.

Answer 1

The period of time can be calculated by using following formula
Present Value Of Annuity
c= Cash Flow	750
i= Interest Rate	0.66667%
n= Number Of Periods	1
Present Value Of An Annuity
= C*[1-(1+i)^-n]/i]
Where,
C= Cash Flow per period
i = interest rate per period
n=number of period
$52000= $750[ 1-(1+0.006666667)^-n /0.006666667]
$52000= $750[ 1-(1.006666667)^-n /0.006666667]
$52000/750 =[ 1-(1.006666667)^-n /0.006666667]
n = 93.36
Number of months = 93.36
Number of years =93.36/12 =7.78 years