Question

Today, Malorie takes out a 30-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 30 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 30 years.

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

Answer 1

C)

Please see the below formula to calculate interest rate.

EMI = [P x R x (1+R)^N] / [((1+R)^N)-1], where P stands for the loan amount or principal,

R is the interest rate per month [if the interest rate per annum is 4.5%, then the rate of interest will be 4.5/(12 x 100)], and N is the number of monthly instalments

Let us pick one by one.

P = $200,000 (given on the question)

R = 4.5/(12*100) = 0.00375

N = 30 Years, when we convert 30 years to Months it should be 30*12 = 360

EMI = [$200000*0.00375*(1+.00375)^360] / [((1+.00375)^360)-1]

= $ 1013.37

He paid total value of $ 1013.37 * 360 = $ 364813.42

that means he paid $ 364813.42 - $ 200000 = $164813.42 as total interest for 30 years.

Here the question is how much interest he paid on three years (fixed interest period). Please see the below table to know the detailed explanation.

As per below total interest paid for 3 years is $ 26,350.51

No of Months	Principal	EMI	Rate	Interest	Principal Amt
1	$                                     200,000.00	$     1,013.37	0.00375	$          750.00	$           263.37
2	$                                     199,736.63	$     1,013.37	0.00375	$          749.01	$           264.36
3	$                                     199,472.27	$     1,013.37	0.00375	$          748.02	$           265.35
4	$                                     199,206.92	$     1,013.37	0.00375	$          747.03	$           266.34
5	$                                     198,940.58	$     1,013.37	0.00375	$          746.03	$           267.34
6	$                                     198,673.24	$     1,013.37	0.00375	$          745.02	$           268.35
7	$                                     198,404.89	$     1,013.37	0.00375	$          744.02	$           269.35
8	$                                     198,135.54	$     1,013.37	0.00375	$          743.01	$           270.36
9	$                                     197,865.18	$     1,013.37	0.00375	$          741.99	$           271.38
10	$                                     197,593.80	$     1,013.37	0.00375	$          740.98	$           272.39
11	$                                     197,321.41	$     1,013.37	0.00375	$          739.96	$           273.41
12	$                                     197,047.99	$     1,013.37	0.00375	$          738.93	$           274.44
13	$                                     196,773.55	$     1,013.37	0.00375	$          737.90	$           275.47
14	$                                     196,498.09	$     1,013.37	0.00375	$          736.87	$           276.50
15	$                                     196,221.58	$     1,013.37	0.00375	$          735.83	$           277.54
16	$                                     195,944.04	$     1,013.37	0.00375	$          734.79	$           278.58
17	$                                     195,665.46	$     1,013.37	0.00375	$          733.75	$           279.62
18	$                                     195,385.84	$     1,013.37	0.00375	$          732.70	$           280.67
19	$                                     195,105.17	$     1,013.37	0.00375	$          731.64	$           281.73
20	$                                     194,823.44	$     1,013.37	0.00375	$          730.59	$           282.78
21	$                                     194,540.66	$     1,013.37	0.00375	$          729.53	$           283.84
22	$                                     194,256.82	$     1,013.37	0.00375	$          728.46	$           284.91
23	$                                     193,971.91	$     1,013.37	0.00375	$          727.39	$           285.98
24	$                                     193,685.93	$     1,013.37	0.00375	$          726.32	$           287.05
25	$                                     193,398.89	$     1,013.37	0.00375	$          725.25	$           288.12
26	$                                     193,110.76	$     1,013.37	0.00375	$          724.17	$           289.20
27	$                                     192,821.56	$     1,013.37	0.00375	$          723.08	$           290.29
28	$                                     192,531.27	$     1,013.37	0.00375	$          721.99	$           291.38
29	$                                     192,239.89	$     1,013.37	0.00375	$          720.90	$           292.47
30	$                                     191,947.42	$     1,013.37	0.00375	$          719.80	$           293.57
31	$                                     191,653.85	$     1,013.37	0.00375	$          718.70	$           294.67
32	$                                     191,359.18	$     1,013.37	0.00375	$          717.60	$           295.77
33	$                                     191,063.41	$     1,013.37	0.00375	$          716.49	$           296.88
34	$                                     190,766.53	$     1,013.37	0.00375	$          715.37	$           298.00
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