Question

You want to buy a car, and the bank will lend you $20,000. The loan will be fully amortized over five years. Nominal interest rate will be 6% with interest paid monthly. What will be the loan monthly payment. How much of the second month payment will be interest?

Answer 1

the monthly loan payment will be

=>(L * I) * (1 + I)^N / [ (1+I)^N] - 1

here,

L = $20,000.

I = 6% / 12 => 0.5% =>0.005.

N = 5 years * 12 months =>60 months.

now,

($20,000 * 0.005) * (1.005)^60 / [(1.005)^60] - 1

=>($100) * (1.34885015) / 0.34885015

=>$386.66.

monthly loan payment = $386.66.

to know the interest payment in second payment we shall prepare an extract of amortization schedule.

month	opening balance	interest on opening balance #@0.5%	EMI payment	Principal paid	closing balance
1	20,000	100	386.66	386.66-100=>286.66	20,000-286.66=>19713.34
2	19,713.34	98.57	386.66	386.66-98.57=>288.09	19,425.21

Therefore interst paid in second month =$ 98.57.