Question

Assume a mortgage loan amount of $ 300,000, with annual interest rate 4% and 5 years term 1. Calculate annual payment amount 2. Calculate monthly payment amount 3. Do you pay more annually or monthly? Why? 4. Prepare a 60 month loan amortization schedule. How much is your total interest payment?

Answer 1

1) Loan Amount = $300,000

Annual Payment Amount = Loan Amount/PVAF(4%, 5 yrs)

= $300,000/4.45182 = $67,388

2) Monthly Interest Rate = 4%*1/12 = 1/3% or 0.3333%

No. of periods = 5 years*12 months per year = 60

Monthly Payment = Loan Amount/PVAF(0.33333%, 60)

= $300,000/54.299069 = $5,525

3) Total payment annually = Annual payment*5 years

= $67,388*5 = $336,940

Total payment monthly = Monthly Payment*60 months

= $5,525*60 = $331,500

The amount paid annually of $336,940 is more than the amount paid monthly of $331,500.

4) Loan Amortization Schedule (Amounts in $)

Months	Beg. Loan balance (A)	Amount Paid (B)	Interest Expense (C = A*0.33333%)	Decrease in Loan Balance (D = B - C)	Closing Balance Loan (A - D)
1	300,000	5,525	1,000	4,525	295,475
2	295,475	5,525	985	4,540	290,935
3	290,935	5,525	970	4,555	286,380
4	286,380	5,525	955	4,570	281,810
5	281,810	5,525	939	4,586	277,224
6	277,224	5,525	924	4,601	272,623
7	272,623	5,525	909	4,616	268,007
8	268,007	5,525	893	4,632	263,375
9	263,375	5,525	878	4,647	258,728
10	258,728	5,525	862	4,663	254,065
11	254,065	5,525	847	4,678	249,387
12	249,387	5,525	831	4,694	244,693
13	244,693	5,525	816	4,709	239,984
14	239,984	5,525	800	4,725	235,259
15	235,259	5,525	784	4,741	230,518
16	230,518	5,525	768	4,757	225,761
17	225,761	5,525	753	4,772	220,989
18	220,989	5,525	737	4,788	216,201
19	216,201	5,525	721	4,804	211,397
20	211,397	5,525	705	4,820	206,577
21	206,577	5,525	689	4,836	201,741
22	201,741	5,525	672	4,853	196,888
23	196,888	5,525	656	4,869	192,019
24	192,019	5,525	640	4,885	187,134
25	187,134	5,525	624	4,901	182,233
26	182,233	5,525	607	4,918	177,315
27	177,315	5,525	591	4,934	172,381
28	172,381	5,525	575	4,950	167,431
29	167,431	5,525	558	4,967	162,464
30	162,464	5,525	542	4,983	157,481
31	157,481	5,525	525	5,000	152,481
32	152,481	5,525	508	5,017	147,464
33	147,464	5,525	492	5,033	142,431
34	142,431	5,525	475	5,050	137,381
35	137,381	5,525	458	5,067	132,314
36	132,314	5,525	441	5,084	127,230
37	127,230	5,525	424	5,101	122,129
38	122,129	5,525	407	5,118	117,011
39	117,011	5,525	390	5,135	111,876
40	111,876	5,525	373	5,152	106,724
41	106,724	5,525	356	5,169	101,555
42	101,555	5,525	339	5,186	96,369
43	96,369	5,525	321	5,204	91,165
44	91,165	5,525	304	5,221	85,944
45	85,944	5,525	286	5,239	80,705
46	80,705	5,525	269	5,256	75,449
47	75,449	5,525	251	5,274	70,175
48	70,175	5,525	234	5,291	64,884
49	64,884	5,525	216	5,309	59,575
50	59,575	5,525	199	5,326	54,249
51	54,249	5,525	181	5,344	48,905
52	48,905	5,525	163	5,362	43,543
53	43,543	5,525	145	5,380	38,163
54	38,163	5,525	127	5,398	32,765
55	32,765	5,525	109	5,416	27,349
56	27,349	5,525	91	5,434	21,915
57	21,915	5,525	73	5,452	16,463
58	16,463	5,525	55	5,470	10,993
59	10,993	5,525	37	5,488	5,505
60	5,505	5,525	20 (5,525-5,505)	5,505	0
Total		331,500	31,500	300,000

In the 60th month, the interest is taken as balancing figure to avoid rounding off difference.

Thus the total amount of interest paid is $31,500.