Question

Hybrid ARM. We have a mortgage with the following characteristics:
Issued at 80% LTV on a $150,000 property
3/1 Hybrid Loan
30 years maturity with monthly payments
Fully Amortizing
Initial Mortgage Rate 6%
Mortgage rate adjusts to LIBOR plus a margin of 180bp
At the first reset LIBOR is at 3%

A. What is the scheduled payment in the first month?

B. What fraction of the scheduled payment in the first month goes to pay principal? What fraction of the scheduled payment in the first month goes to pay
interest? Write both numbers (in either fraction or percentage).

C. What is the mortgage balance when the mortgage rate first resets?

D. What is the new mortgage rate (annual) when it first resets?

E. What is the first scheduled payment when the mortgage rate first resets?

please show steps

Answer 1

A. Value of property = = 150000 , LTV of the property = 80%

Loan on the property = 80% of 150000 = 120000

Since it is 3/1 Hybrid hence first interest rate reset will be after 3 years

Initial rate = 6% per year, Amortization period = 30 years = 30 x 12 = 360 months

Monthly rate = initial per year rate / 12 = 6%/12 = 0.50%

We will use pmt function in excel to calculate monthly payment for first three years:

Formula to be used in excel =pmt(rate,nper,-pv)

Below in excel screen shot of calculation

Using pmt function in excel, we get monthly payments for first three years = 719.46

Hence scheduled payment in first month = 719.46

B. We know that interest for a month = Beginning balance of month x monthly interest rate

Principal for a month = Monthly payment - interest for the month

Ending balance of a month = Beginning balance of a month - principal for a month

Beginning balance for a month = Ending balance of previous month

For first month

Beginning balance = 120000, interest = 120000 x 0.50% = 600, Principal = 719.46 - 600 = 119.46, Ending balance = 120000 - 119.46 = 119880.54

Fraction of scheduled payment in 1st that goes toward principal = Principal for 1st month / monthly payment = 119.46 / 719.46 = 16.60%

Fraction of scheduled payment in 1st that goes toward interest = interest for 1st month / monthly payment = 600 / 719.46 = 83.40%

C. To find the mortgage balance at the end at first reset (after 36 months), we will have build amortization schedule for other months also using the formulae used par B.

For 2nd month

Beginning balance for 2nd month = Ending balance of 1st month = 119880.54

Interest = 119880.54 x 0.50% = 599.40, Principal = 719.46 - 599.40 = 120.06 ,Ending balance = 119880.54 - 120.06 = 119760.48

. Similarly values can be found out for other months using the formulae

We get following amortization schedule for first 36 months

Month	Beginning Balance	Monthly Payment	Interest	Principal	Ending Balance
1	120000.00	719.46	600.00	119.46	119880.54
2	119880.54	719.46	599.40	120.06	119760.48
3	119760.48	719.46	598.80	120.66	119639.83
4	119639.83	719.46	598.20	121.26	119518.56
5	119518.56	719.46	597.59	121.87	119396.70
6	119396.70	719.46	596.98	122.48	119274.22
7	119274.22	719.46	596.37	123.09	119151.13
8	119151.13	719.46	595.76	123.70	119027.43
9	119027.43	719.46	595.14	124.32	118903.10
10	118903.10	719.46	594.52	124.94	118778.16
11	118778.16	719.46	593.89	125.57	118652.59
12	118652.59	719.46	593.26	126.20	118526.39
13	118526.39	719.46	592.63	126.83	118399.57
14	118399.57	719.46	592.00	127.46	118272.10
15	118272.10	719.46	591.36	128.10	118144.00
16	118144.00	719.46	590.72	128.74	118015.26
17	118015.26	719.46	590.08	129.38	117885.88
18	117885.88	719.46	589.43	130.03	117755.85
19	117755.85	719.46	588.78	130.68	117625.17
20	117625.17	719.46	588.13	131.33	117493.83
21	117493.83	719.46	587.47	131.99	117361.84
22	117361.84	719.46	586.81	132.65	117229.19
23	117229.19	719.46	586.15	133.31	117095.88
24	117095.88	719.46	585.48	133.98	116961.90
25	116961.90	719.46	584.81	134.65	116827.25
26	116827.25	719.46	584.14	135.32	116691.92
27	116691.92	719.46	583.46	136.00	116555.92
28	116555.92	719.46	582.78	136.68	116419.24
29	116419.24	719.46	582.10	137.36	116281.88
30	116281.88	719.46	581.41	138.05	116143.83
31	116143.83	719.46	580.72	138.74	116005.09
32	116005.09	719.46	580.03	139.43	115865.65
33	115865.65	719.46	579.33	140.13	115725.52
34	115725.52	719.46	578.63	140.83	115584.69
35	115584.69	719.46	577.92	141.54	115443.15
36	115443.15	719.46	577.22	142.24	115300.91

Thus balance when mortgage rate first resets i.e after 36 months = 115300.91

D. LIBOR = 3%

New Mortgage when it resets = LIBOR + 180bp

= LIBOR + (180/100)% = 3% + 1.8% = 4.8% per year                   (where 100 bp = 1%)

E. Loan balance remaining after 36 months = 115300.91, Period of amortization left = 27 years = 27 x 12 months = 324 months. interest rate = 4.8% per year

monthly interest rate = annual interest rate / 12 = 4.8% /12 = 0.40%

We will use pmt function in excel to find scheduled payment when rate resets

Formula to be used in excel: =pmt(rate,nper,-pv)

Using pmt function in excel we get first scheduled payment at first reset = 635.56