Question

You have borrowed $10,000. The loan is a 4 year loan with payments every 3 months and an interest rate of 3% APR. How much interest will you pay in the first three months?

Answer 1

We are given the following information:

r	3.00%
n	4
frequency	4 = 12/3 as payments are every 3 months or quarterly
PV	$       10,000.00

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

Following is the amortization schedule:

Quarter	Opening Balance	Loan	PMT	Interest	Principal repayment	Closing Balance
0		$   10,000.00				$         10,000.00
1	$            10,000.00		$         665.59	$     75.00	$                         590.59	$           9,409.41
2	$              9,409.41		$         665.59	$     70.57	$                         595.02	$           8,814.39
3	$              8,814.39		$         665.59	$     66.11	$                         599.48	$           8,214.91
4	$              8,214.91		$         665.59	$     61.61	$                         603.98	$           7,610.94
5	$              7,610.94		$         665.59	$     57.08	$                         608.51	$           7,002.43
6	$              7,002.43		$         665.59	$     52.52	$                         613.07	$           6,389.36
7	$              6,389.36		$         665.59	$     47.92	$                         617.67	$           5,771.70
8	$              5,771.70		$         665.59	$     43.29	$                         622.30	$           5,149.40
9	$              5,149.40		$         665.59	$     38.62	$                         626.97	$           4,522.43
10	$              4,522.43		$         665.59	$     33.92	$                         631.67	$           3,890.76
11	$              3,890.76		$         665.59	$     29.18	$                         636.41	$           3,254.35
12	$              3,254.35		$         665.59	$     24.41	$                         641.18	$           2,613.17
13	$              2,613.17		$         665.59	$     19.60	$                         645.99	$           1,967.18
14	$              1,967.18		$         665.59	$     14.75	$                         650.83	$           1,316.35
15	$              1,316.35		$         665.59	$       9.87	$                         655.72	$               660.63
16	$                  660.63		$         665.59	$       4.95	$                         660.63	$                    0.00
			$   10,649.41	$ 649.41	$                   10,000.00

Opening balance = previous year's closing balance
Closing balance = Opening balance+Loan-Principal repayment
PMT is calculated as per the above formula
Interest = 0.03 /12 x opening balance
Principal repayment = PMT - Interest

We see that in the 1st quarter, the interest was 75 and the principal portion of the PMT was  $590.59 adding up to  $665.59, therefore, the interest in the 1st 3 months or the 1st quarter was $75.00