Question

A borrower is offered a 30 year, fully amortizing ARM with an initial rate of 3.35%. After the first year, the interest rate will adjust each year, using 1 yr LIBOR as the index, plus a margin of 175bp. The price of the property is $8,000,000 and the loan will have an initial LTV ratio of 75% At the first reset date, 1 year LIBOR is at 3%. What is the borrower s payment during the 2nd year of the loan?

Answer 1

Step 1: Calculating Monthly payment for year 1

Loan = LTV ratio x Price of property = 75% x 8000000 = $6000000

Initial rate = 3.35%, Initial Monthly rate = Initial rate / 12 = 3.35% / 12

Period of loan = 30 years = 12 x 30 months = 360 months

We can find the monthly payment of loan for first year using PMT function in excel

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

Using PMT function in excel, we get monthly loan payment for year 1 = $26442.811856

Step 2: Calculating Loan Balance after 1 year

Loan balance after 1 year can found out using monthly payment calculated above

After 1 year, Period of loan left = 29 years = 12 x 29 = 348 months,

We can find the loan balance after 1 year using PV function in excel

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

Using PV function in excel, we get loan balance after 1 year = $5881883.6333

Step 3: Calculating Monthly payment for year 2

Rate of year 2 = Libor + Margin = 3% + 175 bp = 3% + 1.75% = 4.75%

Monthly rate for year 2 = Rate for year 2 / 12 = 4.75% / 12

Period of loan left = 29years = 348 months

We can find the monthly payment of loan in year 2 using PMT function in excel

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

Using PMT function in excel, we get monthly loan payment in year 2 = $31163.5663 = $31163.57

Monthly loan payment in year 2 = $31163.57