Property value is $350,000, 5-1ARM, term: 5-30, interest rate 3.5%,required percent down 20%, closing costs 4500,...

Property value is $350,000, 5-1ARM, term: 5-30, interest rate 3.5%,required percent down 20%, closing costs 4500, orgination points 1%, ARM rate after adjustment is 5%, increase in rate if 2nd Mortgage used 1.5%

a. If held until maturity, how much interest will be paid?

b. What is the effective borrowing cost?

c. How much will your payment increase if you take out a second mortgage?

Expert Solution

Soln : Property Value = 350000, Downpayment = 20% *350000

Loan value = 80%*350000 = $280000, 5-1 ARM, 5 year fixed rate and after that every year rate is changing at rate of increase in 1%.

Now, if this loan is held until maturity., please refer the calculation in table done in excel.where EMI is calculated using PMT formula = PMT (rate,nper,pv,fv,0)

Till year 5 the EMI remain same , while from year 6 the interest rate will increase by 1% and accordingly the EMI is calculated for each year.

Years	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
Principal	280000	280000	274576.03	268962.22	263151.92	257138.26	250914.13	245283.86	240124.12	235331.05	230815.79	226500.59	222315.61	218195.95	214078.99	209901.78	205598.30	201096.54	196314.98	191158.47	185512.97	179238.72	172161.41	164060.21	154651.80	143568.46	130328.03	114292.36	94609.45	70132.37	39304.95
EMI		15223.97	15223.97	15223.97	15223.97	15223.97	16921.41	18650.36	20401.13	22165.10	23934.54	25702.54	27462.80	29209.49	30937.09	32640.21	34313.52	35951.52	37548.47	39098.24	40594.15	42028.87	43394.28	44681.35	45880.00	46979.02	47966.03	48827.46	49548.59	50113.81	50506.86
Interest		9800.00	9610.16	9413.68	9210.32	8999.84	11291.14	13490.61	15608.07	17649.83	19619.34	21517.56	23343.14	25092.53	26759.87	28336.74	29811.75	31169.96	32391.97	33452.73	34319.90	34951.55	35293.09	35272.95	34796.66	33738.59	31930.37	29144.55	25071.51	19286.40	11201.91
Remaining Principal		274576.03	268962.22	263151.92	257138.26	250914.13	245283.86	240124.12	235331.05	230815.79	226500.59	222315.61	218195.95	214078.99	209901.78	205598.30	201096.54	196314.98	191158.47	185512.97	179238.72	172161.41	164060.21	154651.80	143568.46	130328.03	114292.36	94609.45	70132.37	39304.95	0.00
interest rate		3.50%	3.50%	3.50%	3.50%	3.50%	4.5%	5.5%	6.5%	7.5%	8.5%	9.5%	10.5%	11.5%	12.5%	13.5%	14.5%	15.5%	16.5%	17.5%	18.5%	19.5%	20.5%	21.5%	22.5%	23.5%	24.5%	25.5%	26.5%	27.5%	28.5%

a) Interest paid = Sum of interest paid = $701577 (approx.)

b) Total interest paid in 30 years = 701577, further closing cost of 4500 is also paid. So, Total interest paid = 701577+4500 = 706077

Let r be the interest paid or effective borrowing cost , we can say that (1+r)³⁰ = 1+ 706077/280000

(1+r)³⁰ = 3.52, on solving we get r = 4.28%

c) In case if 2nd mortgage will be considered., EMI = 17803 (Please note we are considering that after 5 years the 2nd mortgage is taken )

Payment increase = 17803 - 15224 = $2579

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