Question

# A debt of 15,000 with interest at the rate of 20% cpd semi-annually, is to be...

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.

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