Question

A 30-year variable-rate mortgage offers a first-year teaser rate of 2%. After that, the rate starts at 4.5%, adjusted based on actual interest rates. The maximum rate over the life of the loan is 10.5%, and the rate can increase by no more than 200 basis points a year. If the mortgage is for $250,000, what is the monthly payment during the first year? Second year? What is the maximum payment during the fourth year? What is the maximum payment ever?

Answer 1

Answer :

The Formula for Present value of bond is :

Where PMT = Peroidic Payment

i = Annual Interest rate

n = number of years

m = Compounding frequency in year

Calculation of monthly payment during the first year

Amount of bond = $250,000

Annual Interest rate = 2%

Number of years = 30

Compounding frequency in year = 12

By putting amounts in above formula :

250,000 = PMT x 270.5

PMT = 250,000 / 270.5 = $924.21

So, monthly payment during the first year = $924.21

Calculation of monthly payment during the second Year

Amount of bond = $250,000

Annual Interest rate = 4.5%

Number of years = 30

Compounding frequency in year = 12

By putting amounts in above formula :

250,000 = PMT x 197.36

PMT = 250,000 / 197.36

PMT = $1,266.72

So, monthly payment during the second Year = $1,266.72

Calculation of monthly payment during the fourth Year

Amount of bond = $250,000

Annual Interest rate = 4.5 + 2 + 2 =8.5%

Number of years = 30

Compounding frequency in year = 12

By putting amounts in above formula :

250,000 = PMT x 130.05

PMT = 250,000 / 130.05

PMT = 1,922.33

So,monthly payment during the fourth Year = $1,922.33

Calculation of maximum payment ever :

Amount of bond = $250,000

Annual Interest rate (Maximum) = 10.5%

Number of years = 30

Compounding frequency in year = 12

By putting amounts in above formula :

250,000 = PMT x 109.32

PMT = 250,000 / 109.32

PMT = 2,286.86

So,maximum payment ever = $2,286.86