Question

A loan of 11000 is made with interest at a nominal annual rate of 12% compounded monthly. The loan is to be repaid by 36 monthly payments of 367.21 over 37 months, starting one month after the loan is made, there being a payment at the end of every month but one. At the end of which month is the missing payment?

For your reference, the answer is at the 17th month.

Answer 1

Let n be the missing payment month

Hence,

11000=367.21/(12%/12)*(1-1/(1+12%/12)^37)-367.21/(1+12%/12)^n

=>367.21/(1+12%/12)^n=367.21/(12%/12)*(1-1/(1+12%/12)^37)-11000

=>367.21/(367.21/(12%/12)*(1-1/(1+12%/12)^37)-11000)=(1+12%/12)^n

=>log(367.21/(367.21/(12%/12)*(1-1/(1+12%/12)^37)-11000))=nlog(1+12%/12)

=>log(367.21/(367.21/(12%/12)*(1-1/(1+12%/12)^37)-11000))/log(1+12%/12)=n

=>n=17.05700