Question

What is the scheduled P&I payment for the first year of a one-year ARM with an initial principal balance of $175,000, an initial maturity of 30 years, the one-year LIBOR rate as its index (currently 2.90%), and a fixed spread of 250 bps? If, one year from ow, the one-year LIBOR rate has fallen to 2.30%, what will be the scheduled P&I payment for the second year?

Answer 1

The table shown below is constructed from Excel formulas PPMT & IPMT for calculation of Principal & Interest. For 1st Year, Principal for the month = PPMT(5.4%/12,Month, 360, -175,000) (360 -> Tenure in Months, 5.4% -> Interest Rate, 175,000 - Loan Amount).Interest for the month = IPMT(5.4%/12,Month, 360, -175,000). Applying, this formulas, Principal payment in first year = $2,401, Interest Payment = $ 9,391. Total P&I = $11,792.

For the second year, Principal is principal at the end of first year i.e. 172,599. Tenure = 29*12 = 348. Interest Rate = 4.8%. Applying the same formula, Principal & Interest for the second year are $2,812 & $8,223 respectively. Total P&I = $11,036.

	Principal	Interest	Interest Rate	Total	Net Principal
1	195.18	787.50	5.40%	982.68	174,805
2	196.06	786.62	5.40%	982.68	174,609
3	196.94	785.74	5.40%	982.68	174,412
4	197.83	784.85	5.40%	982.68	174,214
5	198.72	783.96	5.40%	982.68	174,015
6	199.61	783.07	5.40%	982.68	173,816
7	200.51	782.17	5.40%	982.68	173,615
8	201.41	781.27	5.40%	982.68	173,414
9	202.32	780.36	5.40%	982.68	173,211
10	203.23	779.45	5.40%	982.68	173,008
11	204.14	778.54	5.40%	982.68	172,804
12	205.06	777.62	5.40%	982.68	172,599
1st Year	2,401	9,391		11,792
13	229.24	690.40	4.80%	919.63	172,370
14	230.15	689.48	4.80%	919.63	172,140
15	231.07	688.56	4.80%	919.63	171,909
16	232.00	687.63	4.80%	919.63	171,677
17	232.93	686.71	4.80%	919.63	171,444
18	233.86	685.77	4.80%	919.63	171,210
19	234.79	684.84	4.80%	919.63	170,975
20	235.73	683.90	4.80%	919.63	170,739
21	236.67	682.96	4.80%	919.63	170,503
22	237.62	682.01	4.80%	919.63	170,265
23	238.57	681.06	4.80%	919.63	170,026
24	239.53	680.11	4.80%	919.63	169,787
2nd Year	2,812	8,223		11,036