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

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