Question

Suppose that you are considering taking out an adjustable-rate mortgage with the following terms: Amount borrowed: $350,000 Index rate: Prime Rate (Currently 2.25%) Margin: 200 basis points. Periodic cap: 1.5 percentage points Lifetime cap: 5 percentage points Amortization: 30 years If the interest rate changes at the end of every year and the prime rate increases to 2.60% during the first year, what will your monthly payment be in year 2? Assume that the lender will use monthly compounding.

Answer 1

Monthly payment for year 2 is $1,782.64

Step-by-step explanation:

According to the given data we have the following:

Mortgage amount .initial balance.(P) =$350,000

Initial interest rate=Prime rate + 200 basis points or 2%

2.25%+2%= 4.25%

Monthly rate 4.25%/12=0.003541666667

no of months (n)=30*12=360

To calculate the monthly payment be in year 2 we would have to use first the monthly payment formula as follows:

Monthly payment = P*i/(1-((1+i)^-n))

=350000*0.00354166667/(1-((1+0.00354166667)^-360))

=$1721.78962

Peroidic cap is 1.5%. it means rate cannot exceed 1.5% by previous adjusted rate

Interest rate for 2nd year =2.60%+2%=4.60%

increase in rate compared to previous year is not more than 1.5%. so interest rate=4.60%

Monthly rate 4.6%/12= 0.003833333333

no of months remaining (n)=29*12=348

First find closing balance at year 1

Unpaid balance at year 1 formula (P)=monthly payment *(1-((1+i)^-n))/i

1721.79*(1-((1+0.003541666667)^-288))/0.003541666667

310532.1673

Therefore, monthly payment in year 2= 310532.1673*0.0038333333/(1-((1+0.00383333333)^-288))

=1782.643774

Monthly payment for year 2 is $1,782.64