Question

Mr. Green took a loan of $10,000 to buy a used car for his son. The interest rate on the loan was 12% per year, and the lender agreed to take an annual payment for 5 years. What is the amount of principal he paid at the time of the second payment?

Please show solution

Answer 1

Basically we need to amortize the loan of $ 10000 where the interest rate is 12% and the maturity of the loan in after 5 years.

We are given the following information:

PMT	Need to find out
r	12.00%
n	5
frequency	1 (Annual)
PV	$     10,000.00

We need to solve the following equation to arrive at the required PV

Now that we know the annual PMT which includes the interest and the principal repayment, we need to complete the following table:

Year	Opening balance	Loan	PMT	Interest	Principal	Closing balance
0	$                            -	$ 10,000.00				$          10,000.00
1	$            10,000.00		$ 2,774.10	$      1,200.00	$ 1,574.10	$            8,425.90
2	$               8,425.90		$ 2,774.10	$      1,011.11	$ 1,762.99	$            6,662.91
3	$               6,662.91		$ 2,774.10	$         799.55	$ 1,974.55	$            4,688.37
4	$               4,688.37		$ 2,774.10	$         562.60	$ 2,211.49	$            2,476.87
5	$               2,476.87		$ 2,774.10	$         297.22	$ 2,476.87	$ 0.00

• Opening balance = previous year's closing balance
• Closing balance = Opening balance+Loan-Principal repayment
• PMT is calculated as per the above formula
• Interest = 12% x opening balance
• Principal repayment = PMT - Interest
• So at the time of second payment, the principal amount repaid is $1762.99