Question

A car loan in the amount of $32,000 will be repaid over a five year term. The rate on the loan is 6%, and payments are compounded monthly. Determine the balance on the loan at the end of month 3.

Answer 1

EMI = P*i*[(1+i)^n]/[{(1+i)^n}-1]

Where,

P = Principal = 32000

i = Interest Rate = 0.06/12 = 0.005

n = Number of periods = 5*12 = 60

Therefore, EMI = 32000*0.005*[(1+0.005)^60]/[{(1+0.005)^60}-1]

= 160*(1.34885)/[1.34885-1] = $618.65

Amortization Schedule:

Period	Opening Principal (previous closing)	Interest (opening*0.005)	Installment	Principal Repayment (installment-interest)	Closing Principal (opening-principal repayment)
1	32000	160	618.65	458.65	31541.35
2	31541.35	157.70675	618.65	460.94325	31080.40675
3	31080.40675	155.4020338	618.65	463.2479663	30617.15878

Therefore, Balance at the end of 3rd month = $30617.16