Question

You want to borrow $22,425. You must repay the loan in 12 years in equal monthly payments and a single $2,894 payment at the end of 12 years. Interest rate is 14% nominal per year.What will be the loan balance immediately after the 50th payment?

Answer 1

PV of Loan = 22,425
PV of Single payment end of 12 years = 2894/(1+14%/12)^12*12 = 544.64

PV of amount for Equal Monthly Payment =  22,425-544.64 = 21,880.36
Periodic Monthly payment = 21,880.36/(1-(1+14%/12)^-144)/(14%/12) = 314.45

Amount of Principal remaining after 50 th payment = PV *(1+r)ⁿ -PMT*((1+r)ⁿ-1)/r =21,880.36*(1+14%/12)⁵⁰- 314.45*((1+14%/12)⁵⁰-1)/(14%/12) = 17893.67

Please Discuss in case of Doubt

Best of Luck. God Bless
Please Rate Well