Question

Mr. and Mrs. Kim purchased a 1 billion KRW house a year ago in Seoul. They took a 10-year mortgage for 600 million KRW at a 5.0% annual interest rate. They have just made their first annual payment. What is the balance of the Kim’s current mortgage right after the first payment? Include the mortgage table that shows the annual mortgage payments, the amount of annual interest payments, the amount of principal paid per year, and the balance of the mortgage during the 10-year period. It is assumed that payments are made at the end of each year and the first payment was made at the end of the first year.

Answer 1

We are given the following information:

Rate of interest	r	5.00%
Number of years	n	10
Annual	frequency	1
Loan amount	PV	$    600,000,000.00

We need to solve the following equation to arrive at the required annual payment or PMT:

PV = PMT x 1-(1+r)-n 600000000 = PMT X- Du 1 - (1 +0.05) -10 0.05 PMT = 77702744.98

So the annual payment is 77,702,744.98

Below is the amortization schedule:

Year	Opening Balance	PMT	Interest	Principal repayment	Closing Balance
1	$   600,000,000.00	$     77,702,744.98	$  30,000,000.00	$47,702,744.98	$  552,297,255.02
2	$   552,297,255.02	$    77,702,744.98	$ 27,614,862.75	$50,087,882.23	$ 502,209,372.79
3	$   502,209,372.79	$     77,702,744.98	$ 25,110,468.64	$52,592,276.34	$   449,617,096.45
4	$   449,617,096.45	$     77,702,744.98	$     22,480,854.82	$55,221,890.16	$   394,395,206.30
5	$   394,395,206.30	$      7,702,744.98	$     19,719,760.31	$57,982,984.66	$   336,412,221.63
6	$   336,412,221.63	$     77,702,744.98	$     16,820,611.08	$60,882,133.90	$   275,530,087.73
7	$   275,530,087.73	$     77,702,744.98	$     13,776,504.39	$63,926,240.59	$   211,603,847.14
8	$   211,603,847.14	$77,702,744.98	$     10,580,192.36	$67,122,552.62	$   144,481,294.52
9	$   144,481,294.52	$77,702,744.98	$       7,224,064.73	$70,478,680.25	$     74,002,614.27
10	$74,002,614.27	$77,702,744.98	$       3,700,130.71	$74,002,614.27	-
		$777,027,449.79	$177,027,449.79	$600,000,000.00

Opening balance = previous year's closing balance
Closing balance = Opening balance+Loan-Principal repayment
PMT is calculated as per the above formula
Interest = 0.05 /12 x opening balance
Principal repayment = PMT - Interest
So after 1st payment, the closing balance of loan is  $552,297,255.02

Below is the chart of interest and principal repayment: