Question

----- ------souwu wuuwu Ut ble alla In a standard Amortization Table for the repayment of a loan, the principal · reduction in the 4" payment is $110.81, and the principal reduction in the 10th payment is $206.38. There are 15 payments. b. Determine the annual payment amount. . c. Determine the amount of the loan d. Find the outstanding balance immediately after the gth payment..

Answer 1

To find the relation between portion of principle payment in amortisation schedule, we take an assumed schedule of amortisation as below:

Total Loan Amount= 152

15 Installments

Interest = 10% pa

Installments	Amortisation	Opening Balance	Principle	Interest	Closing Balance	Increase in Principle Portion
1	20	152.00	4.80	15.20	147.20
2	20	147.20	5.28	14.72	141.92	10%
3	20	141.92	5.81	14.19	136.11	10%
4	20	136.11	6.39	13.61	129.72	10%
5	20	129.72	7.03	12.97	122.70	10%
6	20	122.70	7.73	12.27	114.97	10%
7	20	114.97	8.50	11.50	106.46	10%
8	20	106.46	9.35	10.65	97.11	10%
9	20	97.11	10.29	9.71	86.82	10%
10	20	86.82	11.32	8.68	75.50	10%
11	20	75.50	12.45	7.55	63.05	10%
12	20	63.05	13.69	6.31	49.36	10%
13	20	49.36	15.06	4.94	34.29	10%
14	20	34.29	16.57	3.43	17.72	10%
15	20	17.72	18.23	1.77	-0.51	10%

We observe, principle portion increases by 10% which is the given rate of interest

Hence for every year principle portion increases by the Interest Rate

Given the 4th Installment Amount and 10th Instalment Amount

So 4th Instalment would increase by x% for 6 years

i.e 110.81 (1*x%)^6= 206.38

i.e x = 10.92%

a)Rate of Interest = 10.92%

• We redraw the table with plotting the principle amounts of all year considering 10.92% increase year on year. Foe eg. Principle payment for year 5 = Year 4 principle *(1+10.92%) likewise when we go or previous year we reduce by 10.92%
• Then we take the sum of all principle payments, we get actual loan amount i.e 2776.05 (Part c Ans)
• We calculate interest for 1st Year @ 10.92% on 2776.05, we get 303.18
• Annual Payment for 1 st year = Principle for 1st Year+ Interest for 1 st Year = 384.38( Part b Ans)

Installments	Amortisation	Opening Balance	Principle	Interest	Closing Balance	Increase in Principle Portion
1	384.38	2,776.05	81.20	303.18	2,694.85
2	384.38	2,694.85	90.06	294.31	2,604.78	11%
3	384.38	2,604.78	99.90	284.47	2,504.88	11%
4	384.38	2,504.88	110.81	273.56	2,394.06	11%
5	384.38	2,394.06	122.91	261.46	2,271.14	11%
6	384.38	2,271.14	136.34	248.04	2,134.80	11%
7	384.38	2,134.80	151.22	233.15	1,983.57	11%
8	384.38	1,983.57	167.74	216.63	1,815.82	11%
9	384.38	1,815.82	186.06	198.31	1,629.75	11%
10	384.38	1,629.75	206.38	177.99	1,423.35	11%
11	384.38	1,423.35	228.92	155.45	1,194.42	11%
12	384.38	1,194.42	253.92	130.45	940.49	11%
13	384.38	940.49	281.65	102.71	658.82	11%
14	384.38	658.82	312.41	71.95	346.39	11%
15	384.38	346.39	346.53	37.83	-0.16	11%

Part d Ans) Amount o.s end of year 8 1815.82