Question

Patricia must repay a loan of RM 2800 over 20 years. She has planned to make payments of RM 230 at the end of each year. A portion of the payment will be used to
pay for the interest and the remaining will be deposited into a sinking fund. The lender is charging her 6% of interest on the original loan for the first 12 years, and 4% for the remaining years. The sinking fund is earning a rate of 3%. What is the value in the sinking fund at the end of the 20th year? Show all your calculations. Then briefly explain, the ability of the sinking fund to repay the loan.

Answer 1

Loan amount = 2,800

Duration of loan = 20 years

Payment every year = 230

Rate of interest on loan amount is 6% for first 12 years while it is 4% for next 8 years.

Sinking fund earns 3% rate of interest

Interest for first 12 years is 2,800 * 0.06 while for next 8 years it is 2,800 * 0.4

Sinking fund = Payment - Interest

Future amount of sinking fund is calculated as: [Sinkinf fund * (1 + Rate of Interest)^^{Year for which it earns rate of interest}]

Year	Payment	Interest	Sinking Fund	Interest earned on Sinking funds for years	Future amount of Sinking Fund
1	230	168	62	19	108.7
2	230	168	62	18	105.6
3	230	168	62	17	102.5
4	230	168	62	16	99.5
5	230	168	62	15	96.6
6	230	168	62	14	93.8
7	230	168	62	13	91.0
8	230	168	62	12	88.4
9	230	168	62	11	85.8
10	230	168	62	10	83.3
11	230	168	62	9	80.9
12	230	168	62	8	78.5
13	230	112	118	7	145.1
14	230	112	118	6	140.9
15	230	112	118	5	136.8
16	230	112	118	4	132.8
17	230	112	118	3	128.9
18	230	112	118	2	125.2
19	230	112	118	1	121.5
20	230	112	118	0	118.0
					2163.9

This fund have the ability to repay 2,163.9 of the total loan of 2,800 after 20 years.