Question

A debt of 15,000 with interest at the rate of 20% cpd semi-annually, is to be amortized by 5 equal payments at the end of each 6 months, but the first payment is to be made after 3 years. Find the semi-annual payment and construct the amortization schedule.

Answer 1

Nominal semi-annual interest = 20%/2 = 10%

Loan amount (P) = $15000

Time (n)= 5 equal semi-annual installment ( first payment is at the end of year3)

Let, each semi-annual payment = X

Then

15000 = X/(1+10%)^6 + X/(1+10%)^7 + X/(1+10%)^8 + X/(1+10%)^9 + X/(1+10%)^10

15000 = X*(1/(1+10%)^6 + 1/(1+10%)^7 + 1/(1+10%)^8 + 1/(1+10%)^9 + 1/(1+10%)^10)

15000 = X*2.3538

X = 15000/2.3538

X= $6372.67

So, each six monthly installment will be $6372.67.

For loan amortization schedule:

Loan amount after 5 bi-annual period (2.5 years) = 15000*1.1^5 = $24157.65

R = 10%

Amortization schedule is as follows.

S.No..	six monthly instalment	Interest paid	Principal paid	Loan amount left for the payment
1	6372.67	2415.77	3956.91	20200.75
2	6372.67	2020.07	4352.60	15848.15
3	6372.67	1584.81	4787.86	11060.29
4	6372.67	1106.03	5266.64	5793.65
5	6372.67	579.37	5793.30	0.35