Question

Consider a loan of $225,000 at nominal interest rate of 6.25% for 15 years. How much of the payment during the first year goes towards interest? Assume monthly payments.

		$19,929
		$13,509
		$13,987
		$13,798

Answer 1

$13,798

Working:

Step-1:Calculation of monthly payment
	Monthly payment		=	Loan amount /Present value of annuity of 1
			=	$       2,25,000	/	116.631532
			=	$       1,929.15
Working;
Present value of annuity of 1			=	(1-(1+i)^-n)/i			Where,
			=	(1-(1+0.005208)^-180)/0.005208			i	6.25%/12	=	0.005208
			=	116.6315322			n	15*12	=	180
Step-2:Preparation of first year amortization
Months	Beginning loan		Monthly payment		Monthly interest		Reduction in principal			Ending Loan amount
	a		b		c=a*6.25%*1/12		d=b-c			e=a-d
1	$       2,25,000		$         1,929		$         1,172		$           757			$ 2,24,242.72
2	2,24,243		1,929		1,168		761			2,23,482
3	2,23,482		1,929		1,164		765			2,22,716
4	2,22,716		1,929		1,160		769			2,21,947
5	2,21,947		1,929		1,156		773			2,21,174
6	2,21,174		1,929		1,152		777			2,20,397
7	2,20,397		1,929		1,148		781			2,19,616
8	2,19,616		1,929		1,144		785			2,18,830
9	2,18,830		1,929		1,140		789			2,18,041
10	2,18,041		1,929		1,136		794			2,17,247
11	2,17,247		1,929		1,131		798			2,16,450
12	2,16,450		1,929		1,127		802			2,15,648
Total			23,150		13,798		9,352
Thus,
Total interest payment in the year 1 is				$     13,798