Question

2. Consider a PLAM with the following features:

Mortgage amount	$190,000
Mortgage term	30 years
Current real rate	5%
Inflation for the next 3 years respectively	2%, 3%, 5%
Mortgage payments adjusted annually

1. What are the monthly payments for each of the first 3 years?

2. What is the effective cost if the loan is repaid at the end of year 3?

3. What is the effective cost if the loan is repaid at the end of year3 and the lender charges 2 discount points up front?

Answer 1

Monthly payment in first year 1 = Loan * Monthly interest rate* (1+ monthly interest rate)^n / (1+ monthly interest rate)^n -1

here n= total tenure in months = 30 *12 = 360

Monthly interest in first year = (5% +2%) /12 = 0.5833%

Monthly payment in first year 1 = (190,000 * 0.5833% * (1+0.5833%)^360) / ((1+0.5833%)^360-1)

= $1,264

In the second year Monthly interest rate changes (due to inflation rate) = (5% +3%)/12 = 8% = 0.6667%

Monthly payment in first year 2 = (188,070 * 0.6667% * (1+0.0.6667%)^348) / ((1+0.0.6667%)^348-1)

= $1,392

Similarly monthly payment in year 3 = $1,665

2. Total interest payment during 3 years = 46,800

Loan principal = 190,000

Effective cost per year = 46,800 / 190,000 /3 = 8.2%

3. If lender charges 2 discount point for prepayment, then Effective cost = 46000+(2% * 190000) = $50,600

Effective cost per year = 50,600 / 190,000 /3 = 8.9%

Excel calculations:

	Amortization schedule
	Loan amount	190000
	Terms in months	360
	Current real rate	5%
	Inflation first year	2%
	Annual interest rate	7%
	Monthly interest rate	0.58333%
	Loan beginning balance	Monthly payment	Interest	Principal payment	Loan ending balance
1	190,000	1,264	1,108	156	189,844
2	189,844	1,264	1,107	157	189,688
3	189,688	1,264	1,107	158	189,530
4	189,530	1,264	1,106	158	189,372
5	189,372	1,264	1,105	159	189,212
6	189,212	1,264	1,104	160	189,052
7	189,052	1,264	1,103	161	188,891
8	188,891	1,264	1,102	162	188,728
9	188,728	1,264	1,101	163	188,565
10	188,565	1,264	1,100	164	188,401
11	188,401	1,264	1,099	165	188,236
12	188,236	1,264	1,098	166	188,070
	Interest rate changes to	8.0%
	Monthly interest rate	0.6667%
13	188,070	1,392	1,254	138	187,932
14	187,932	1,392	1,253	139	187,793
15	187,793	1,392	1,252	140	187,654
16	187,654	1,392	1,251	141	187,513
17	187,513	1,392	1,250	142	187,372
18	187,372	1,392	1,249	142	187,229
19	187,229	1,392	1,248	143	187,086
20	187,086	1,392	1,247	144	186,941
21	186,941	1,392	1,246	145	186,796
22	186,796	1,392	1,245	146	186,650
23	186,650	1,392	1,244	147	186,502
24	186,502	1,392	1,243	148	186,354
	Interest rate changes to	10.0%
	Monthly interest rate	0.8%
25	186,354	1,655	1,553	102	186,252
26	186,252	1,655	1,552	103	186,150
27	186,150	1,655	1,551	104	186,046
28	186,046	1,655	1,550	104	185,942
29	185,942	1,655	1,550	105	185,837
30	185,837	1,655	1,549	106	185,730
31	185,730	1,655	1,548	107	185,623
32	185,623	1,655	1,547	108	185,516
33	185,516	1,655	1,546	109	185,407
34	185,407	1,655	1,545	110	185,297
35	185,297	1,655	1,544	111	185,187
36	185,187	1,655	1,543	112	185,075
Total interest payment			46,800

Excel formula: