Question

A loan of $56,000 is paid off in 36 payments at the end of each month in the following way: Payments of $1400 are made at the end of the month for the first 12 months. Payments of $1400 + x are made at the end of the month for the second 12 months. Payments of $1400 + 2x are made at the end of the month for the last 12 months. What should x be if the nominal monthly rate is 13.6%?

Answer 1

PV of Loan =56000
Number of Periods =36
Rate per month =13.6%/12
Payment in month 12 =1400, payment in second 12 months =1400+x, payment in third months =1400+2x

PV =1400*((1-(1+13.6%/12)^-36)/13.6%/12)=41196.25047
PV of remaining amount of loan =56000-41196.25047 =14803.7495

PV of x and 2x payments
=X*(((1-(1+13.6%/12)^-36)/13.6%/12)/(1+13.6%/12)^12+2*(1-(1+13.6%/12)^-36)/13.6%/12)/(1+13.6%/12)^24)
X*(9.74911+17.01390) =14803.7495
X =552.77