Question

Today, Malorie takes out a 20-year loan of $200,000, with a fixed interest rate of 4.5% per annum compounding monthly for the first 3 years. Afterwards, the loan will revert to the market interest rate.

Malorie will make monthly repayments over the next 20 years, the first of which is exactly one month from today. The bank calculates her current monthly repayments assuming the fixed interest rate of 4.5% will stay the same over the coming 20 years.

(b) Calculate the loan outstanding at the end of the fixed interest period (i.e. after 3 years).
(1 mark)

(c) Calculate the total interest Malorie pays over this fixed interest period.
(1.5 marks)

(d) After the fixed interest period, the market interest rate becomes 5.5% per annum effective. Assuming the interest rate stays at this new level for the remainder of the term of the loan, calculate the new monthly installment.
(1.5 marks)

Answer 1

b) loan amount after 3 years = $180,765 from loan amortization schedule.

c) total interest paid in 3 years = $25,729

d) new monthly instalment = $1,243

nper	240
PV	($180,765.90)
rate p.a	5.5
Monthly instalment	$1,243.47	=PMT(5.5/1200,240,180765)
		=pmt(rate,nper,pv)

notes*

nper	240
PV	($200,000.00)
rate p.a	4.5
Monthly instalment	$1,265.30	=PMT(4.5/1200,240,180765)
		=pmt(rate,nper,pv)

Months	Principal	Principal paid	Interest	EMI
1	$200,000.00	$515.30	$750	$1,265.30
2	$199,484.70	$517.23	$748	$1,265.30
3	$198,967.47	$519.17	$746	$1,265.30
4	$198,448.30	$521.12	$744	$1,265.30
5	$197,927.18	$523.07	$742	$1,265.30
6	$197,404.11	$525.03	$740	$1,265.30
7	$196,879.08	$527.00	$738	$1,265.30
8	$196,352.07	$528.98	$736	$1,265.30
9	$195,823.10	$530.96	$734	$1,265.30
10	$195,292.13	$532.95	$732	$1,265.30
11	$194,759.18	$534.95	$730	$1,265.30
12	$194,224.23	$536.96	$728	$1,265.30
13	$193,687.27	$538.97	$726	$1,265.30
14	$193,148.30	$540.99	$724	$1,265.30
15	$192,607.31	$543.02	$722	$1,265.30
16	$192,064.29	$545.06	$720	$1,265.30
17	$191,519.23	$547.10	$718	$1,265.30
18	$190,972.13	$549.15	$716	$1,265.30
19	$190,422.97	$551.21	$714	$1,265.30
20	$189,871.76	$553.28	$712	$1,265.30
21	$189,318.48	$555.35	$710	$1,265.30
22	$188,763.13	$557.44	$708	$1,265.30
23	$188,205.69	$559.53	$706	$1,265.30
24	$187,646.16	$561.63	$704	$1,265.30
25	$187,084.54	$563.73	$702	$1,265.30
26	$186,520.80	$565.85	$699	$1,265.30
27	$185,954.96	$567.97	$697	$1,265.30
28	$185,386.99	$570.10	$695	$1,265.30
29	$184,816.89	$572.24	$693	$1,265.30
30	$184,244.66	$574.38	$691	$1,265.30
31	$183,670.28	$576.54	$689	$1,265.30
32	$183,093.74	$578.70	$687	$1,265.30
33	$182,515.04	$580.87	$684	$1,265.30
34	$181,934.18	$583.05	$682	$1,265.30
35	$181,351.13	$585.23	$680	$1,265.30
36	$180,765.90	$587.43	$678	$1,265.30
			$25,729
After 3 years	remaining loan = 180,765
	interest = 25,729