Question

7. Tim wants to buy an apartment that costs $1,500,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 4.875%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. Tim anticipates the index to be 2.50% at the time of the 1^st reset.

If the index resets to 2.50% as Tim forecasts, what will his new mortgage payment be in year 4?

8. Tim wants to buy an apartment that costs $1,500,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 3.75%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. The index was 1% at the time of origination and remained at 1% during every rate reset. Tim also had to pay 3.0 points for this loan.

9. Bob got a 30 year Fully Amortizing FRM for $2,500,000 at 4%, except with non-constant payments. For the first 2 years Bob will pay $1,250 per month. The loan will become a fully amortizing mortgage after 2 years. What will be the balance on this mortgage after 2 years?

Answer 1

Apartment value = $ 15,00,000

Loanable amount = $15,00,000 * 85% = $12,75,000

Rate of interest = Teaser Rate + Reset Margin over 1 Year CMT

i.e. 4.875+3.00 = 7.875% (This rate will remain  applicable for 3 years as ARM is 3/1)

Mortgage Payment Calculations:

Mortgage Payment (M) = P[r(1+r)^n/((1+r)^n)-1)]

P= Loan Amount

r = Interest Rate

n= Period

= 12,75,000 [ 0.0785 (1.0785)^30/((1.0785)^30-1)]

= 12,75,000 [0.0785 (9.6517)/((9.6517-1)]

= 12,75,000 * 0.7576/8.6517

= $ 1,11,656 per annum for 30 years if interest rate remain same

However as anticipated by tim market index would be 2.500%

Revised Interest rate will be after 3 years = 4.875+2.500 = 7.375%

Remaining Principle ;

First Year Interest = 12,75,000 * 7.875% = 100406

Principle Payment 1st Year = EMI - Interest = 111656-100406 = 11250

Second Year Interest = (1275000-11250)*7.875% = 99520

Principle Payment 2nd Year = 111656-99520 = 12136

Third Year Interest = (1275000-11250-12136)*7.875% = 98564

Principle Payment 3rd Year = 111656-98564 = 13092

Balance Principle at the 3rd year end = 1275000-11250-12136-13092 = 1238522

4th Year Mortgage payment will be: 1238522* [(0.07375) (1.07375)^27)/1.07375)^27) -1

= 1238522 * [ 0.50367/5.82945 ]

= 107010

Thus from 4th year onwards yearly mortgage payment will be $ 1,07,010

It is assumed that payment will be made on yearly basis.