Question

You want to borrow $44,536. You must repay the loan in 6 years in equal monthly payments and a single $3,319 payment at the end of 6 years. Interest rate is 3% nominal per year.

What will be the loan balance immediately after the 32^th payment?

Answer 1

Loan amount = $44536

Time = 72 months

Monthly rate = 3%/12 = .25%

Amount of payment at the end of 6 years = $3319

Let, monthly loan payment = P

Then,

44536 = P*(1-1/(1+.25%)^72)/.25% + 3319/1.03^6

P = (44536 - 3319/1.03^6)/((1-1/(1+.25%)^72)/.25%)

P = $634.43

So,

The loan balance immediately after the 32^th payment = 44536*(1+.25%)^32 - 634.43*((1+.25%)^32 -1)/.25%

The loan balance immediately after the 32^th payment = $27131.97 or $27132

(Slight difference in answer can be there, due to rounding of the decimal points and or taking value of P as $634.43)