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).

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

(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. Dont round up or down please. Thank you!

Answer 1

EMI = P*i*(1+i)^n/[{(1+i)^n}-1]

Where,

P = Principal = 200000

i= Interest Rate = 0.045/12 = 0.00375

n= Number of periods = 20*12 = 240

Therefore, EMI = 200000*0.00375*(1+0.00375)^240/[{(1+0.00375)^240}-1]

= 750*(2.455466)/[2.455466-1] = 1841.5995/1.455466 = $1265.3

Amortization Schedule for first 3 years:

Period	Opening Principal (previous closing)	Interest (opening*0.00375)	Installment	Principal Repayment (installment-interest)	Closing Principal (opening-principal repayment)
1	200000	750	1265.3	515.3	199484.7
2	199484.7	748.067625	1265.3	517.232375	198967.468
3	198967.468	746.1280036	1265.3	519.171996	198448.296
4	198448.296	744.1811086	1265.3	521.118891	197927.177
5	197927.177	742.2269128	1265.3	523.073087	197404.104
6	197404.104	740.2653887	1265.3	525.034611	196879.069
7	196879.069	738.2965089	1265.3	527.003491	196352.066
8	196352.066	736.3202458	1265.3	528.979754	195823.086
9	195823.086	734.3365717	1265.3	530.963428	195292.122
10	195292.122	732.3454589	1265.3	532.954541	194759.168
11	194759.168	730.3468793	1265.3	534.953121	194224.215
12	194224.215	728.3408051	1265.3	536.959195	193687.256
13	193687.256	726.3272082	1265.3	538.972792	193148.283
14	193148.283	724.3060602	1265.3	540.99394	192607.289
15	192607.289	722.2773329	1265.3	543.022667	192064.266
16	192064.266	720.2409979	1265.3	545.059002	191519.207
17	191519.207	718.1970267	1265.3	547.102973	190972.104
18	190972.104	716.1453905	1265.3	549.154609	190422.95
19	190422.95	714.0860607	1265.3	551.213939	189871.736
20	189871.736	712.0190084	1265.3	553.280992	189318.455
21	189318.455	709.9442047	1265.3	555.355795	188763.099
22	188763.099	707.8616205	1265.3	557.43838	188205.66
23	188205.66	705.7712266	1265.3	559.528773	187646.132
24	187646.132	703.6729937	1265.3	561.627006	187084.505
25	187084.505	701.5668924	1265.3	563.733108	186520.772
26	186520.772	699.4528932	1265.3	565.847107	185954.924
27	185954.924	697.3309666	1265.3	567.969033	185386.955
28	185386.955	695.2010827	1265.3	570.098917	184816.856
29	184816.856	693.0632118	1265.3	572.236788	184244.62
30	184244.62	690.9173238	1265.3	574.382676	183670.237
31	183670.237	688.7633888	1265.3	576.536611	183093.7
32	183093.7	686.6013765	1265.3	578.698624	182515.002
33	182515.002	684.4312567	1265.3	580.868743	181934.133
34	181934.133	682.2529989	1265.3	583.047001	181351.086
35	181351.086	680.0665726	1265.3	585.233427	180765.853
36	180765.853	677.8719473	1265.3	587.428053	180178.425 = Loan Outstanding
	Total Interest Paid = [Sum of above Interests]	25729.22455

EMI = P*i*(1+i)^n/[{(1+i)^n}-1]

Where,

P = Principal = 180178.425

i= Interest Rate = 0.055/12 = 0.004583

n= Number of periods = 17*12 = 204

Therefore, New EMI = 180178.425*0.004583*(1+0.004583)^204/[{(1+0.004583)^204}-1]

= 825.81778*(2.541778)/[2.541778-1] = 2099.0455/1.541778 = $1361.44