Question

Encik Ramli borrows RM20,000 and will repay the loan under a 25-year annuity immediate payments. The annual repayment is calculated at an effective interest rate of 8% with increment of RM50 each year.

(i) Calculate the amount of the first payment.

(ii) Calculate the outstanding balance after the first three payments have been made.

(iii) Explain your answer to part (ii)

(iv) Calculate the total amount of interest paid over the term of the loan.

Answer 1

(i) Calculate the amount of the first payment.

Loan Amount	20,000
Tenure (years)	25
Interest rate	8%
Annual payments:
Using excel	1,873.58	=PMT(8%,25,-20000)
Using equation	1,873.58	((20000*8%)*(1+8%)^(25)/((1+8%)^(25)-1))

Thus, amount of first payment = RM 1873.58 or RM1874

(ii) Annual repayment is increased by RM50 each year. With this clause, below is the amortisation schedule:

Payments	Opening Principal	Annual payment	Interest payment	Principal repayment	Closing Principal
1	20,000	1,874	1,600	274	19,726
2	19,726	1,924	1,578	345	19,381
3	19,381	1,974	1,550	423	18,958
4	18,958	2,024	1,517	507	18,451
5	18,451	2,074	1,476	598	17,853
6	17,853	2,124	1,428	695	17,158
7	17,158	2,174	1,373	801	16,357
8	16,357	2,224	1,309	915	15,442
9	15,442	2,274	1,235	1,038	14,404
10	14,404	2,324	1,152	1,171	13,233
11	13,233	2,374	1,059	1,315	11,918
12	11,918	2,424	953	1,470	10,448
13	10,448	2,474	836	1,638	8,810
14	8,810	2,524	705	1,819	6,991
15	6,991	2,574	559	2,014	4,977
16	4,977	2,624	398	2,225	2,751
17	2,751	2,674	220	2,453	298
18	298	322	24	298	-
		38,972	18,972	20,000

(ii) The outstanding balance after the first three payments have been made = RM18,958 (Closing Principal as at payment 3 in above amortisation schedule)

(iii) Calculation of amortisation schedule above is detailed below:

Opening Principal : For year 1, this is loan value of 20,000 and for subsequent years equals Closing Principal of previous year.

Annual payment : Annual payment of 1st payment as computed above is 1874. Annual repayment is increased by RM50 each year. Thus, annual payment of 2nd payment is 1874+50 = 1924 and for third payment is 1924+50 and so on till 17th payment.

Closing principal on 17th payment is 298. So the annual payment of 18th payment will be 298+(298*8%) = 322.

Interest payment : Opening Principal outstanding * 8%

Principal repayment : Annual payment - Interest payment

Closing Principal : Opening Principal - Principal repayment

As can be seen in the above amortisation schedule, though the loan tenure is 25 years, since RM50 is additionally repaid each year, the tenure of the loan reduces to 18 years.

(iv) total amount of interest paid over the term of the loan = RM 18,972 (total of interest payment in above amortisation schedule).

Excel screenshot of amortsation schedule for reference: