Question

Broke National Bank offers you an auto loan to purchase a car. The loan amount is $10,000. The loan amortizes interest over five years of monthly payments. The interest rate is 6% on an annual basis. What is your monthly payment?

N = ________                                       i = ________

FV = $________                                   PV = $________

PMT = $________ per month

Assuming you take the loan described in the prior problem, how much of the initial payment is interest and how much of the initial payment is principle?

Interest Paid in Period One = $________

Principle Paid in Period One = $________

Answer 1

EMI can be calculated using the following formula

P*I*(1+I)^N/[(1+I)^N-1]

Where,

P - Loan amount (here $10,000)

I - Interest rate per month (here 0.5%=0.005 [6%/12])

N - Total no. of installment (here 60 [5*12])

EMI = P*I*(1+I)^N/[(1+I)^N-1]

= $10,000 * 0.005 * 1.005⁶⁰ / (1.005⁶⁰-1)

= 50 * 1.3488 / 0.3488

=$ 193.35

The loan amortisation schedule for the first year is as follows-

Month	Opening Balance	EMI	Interest Paid	Principal Paid	Closing Balnce
1	10,000.00	193.35	50.00	143.35	9,856.65
2	9,856.65	193.35	49.28	144.07	9,712.58
3	9,712.58	193.35	48.56	144.79	9,567.80
4	9,567.80	193.35	47.84	145.51	9,422.29
5	9,422.29	193.35	47.11	146.24	9,276.05
6	9,276.05	193.35	46.38	146.97	9,129.08
7	9,129.08	193.35	45.65	147.70	8,981.37
8	8,981.37	193.35	44.91	148.44	8,832.93
9	8,832.93	193.35	44.16	149.19	8,683.74
10	8,683.74	193.35	43.42	149.93	8,533.81
11	8,533.81	193.35	42.67	150.68	8,383.13
12	8,383.13	193.35	41.92	151.43	8,231.70

Here interest paid = Opening balance * 6% / 12

Principal paid = EMI - interest paid