Question

Five years ago, Mr. K, who runs a restaurant, purchased a nearby site to expand the parking lot for the convenience of customers. For this purpose, 250 million won was loaned from a commercial bank under the condition of repayment of the same amount each year from a floating-rate mortgage product whose repayment interest rate fluctuates every year, and all of it has been repaid over the past five years. At this time, interest rates for five years changed to 5% in the first year, 7.5% in the second year, 10% in the third year, 12.5% in the fourth year and 15% in the fifth year, respectively.

(1) What is the annual real interest rate on this loan?

(2) What is the total interest paid by Mr. D for five years?

Answer 1

(1) Real Interest rate is excess of Nominal interest rate over inflation rate. That is Real interest rate
is the actual interest rate and does not include interest rate as increased due to inflation.
Year	Nominal Interest Rate	Inflation Premium Rate	Real Interest Rate
(a)	(b)	(c )	(d=b-c)
1	5%	0%	5%
2	7.50%	2.50%	5%
3	10%	5.00%	5%
4	12.50%	7.50%	5%
5	15%	10.00%	5%
(2) Loan repaid Sheet
Year	Opening Balance	Interest Rate	Interest	Principal Paid	Closing Balance
(a)	(b)	(c )	(d=b*c )	(e=62.81-d)	(f=b-e)
1	250.00	5.0%	12.50	50.31	199.69
2	199.69	7.5%	14.98	47.83	151.86
3	151.86	10.0%	15.19	47.62	104.23
4	104.23	12.5%	13.03	49.78	54.45
5	54.45	15.0%	8.36	54.45	-0
WN:1) Yearly Payment shall be = Loan Amount/ PVF (cumulative for 5 year at different rate)
Yearly payment = 250 million/(.952+.885+.805+.715+.622)
Yearly payment = 250 million/3.98
62.81	millions