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 first year of loan

Total loan = Initial balance of loan = LTV ratio x Price of property = 75% x 8000000 = 6000000

As payments for loan are made monthly, therefore

Initial monthly rate = Initial rate for year 1 / 12 = 3.35% / 12

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

Now 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 payment of loan in first year or year 1 = $26442.811856

Step 2: Calculating Outstanding Balance after 1 year

We can find the Outstanding balance after 1 year with help of monthly payment calculated above.

Period of loan left after 1 year = 12 x no of years left = 12 x 29 = 348 months

Now we will use PV function in excel to calculate outstanding balance or loan balance after 1 year

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

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

Step 3. Calculating monthly payment for second year

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

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

Period of loan left in months = 12 x period of loan left in years = 12 x 29 = 348 months

We can find the monthly payment of loan in second 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 in second year = $31163.5663 = $31163.57 (rounded to two decimal places)

Monthly loan payment in second year of loan = $31163.57