Question

You borrow $50,000 from your parents. The terms of the loan are that you will make equal payments back to your parents at the end of each of the next 4 years. If the interest rate on the loan is 3% calculate

1) the amount of each payment

2) the amount that you will pay in interest for the four years (total amount of interest). Verify your results by constructing an amortization table.

3) Calculate the payment if instead of annual payments, you make monthly payments.

Answer 1

1)

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

Where,

P = Principal = 50000

i = Interest Rate = 0.03

n = Number of periods = 4

Therefore, EMI = 50000*0.03*[(1+0.03)^4]/[{(1+0.03)^4}-1]

= 1500*(1.1255)/[1.1255-1] = $13451.35

2)

Total Interest = Total of 4 Installments-Principal = (4*13451.35)-50000 = 53805.41-50000 = $3805.41

Amortization Schedule:

Period	Opening Principal (previous closing)	Interest (opening*0.03)	Installment	Principal Repayment (installment-interest)	Closing Principal (opening-principal repayment)
1	50000	1500	13451.35	11951.35	38048.65
2	38048.65	1141.4595	13451.35	12309.8905	25738.7595
3	25738.7595	772.162785	13451.35	12679.18722	13059.57229
4	13059.57229	391.7871686	13451.35	13059.56283	0.00945355
	Total Interest =	3805.409454 = $3805.41

3)

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

Where,

P = Principal = 50000

i = Interest Rate = 0.03/12 = 0.0025

n = Number of periods = 4*12 = 48

Therefore, EMI = 50000*0.0025*[(1+0.0025)^48]/[{(1+0.0025)^48}-1]

= 125*(1.127328)/[1.127328-1] = $1106.72