Question

An Adjustable Rate Mortgage (ARM) is made for $300,000 at an initial interest rate of 2 percent for

30 years. The ARM will be adjusted annually. The borrower believes that the interest rate at the

beginning of the year (BOY) 2 will increase to three percent (3%).

a. Assuming that the ARM is fully amortizing, what will monthly payments be during year 1?

b. Based on (a) what will the loan balance be at the end of year (EOY) 1?

c. Given that the interest rate is expected to be 3 percent at the beginning of year 2, what will

monthly payments be during year 2?

d. What will be the loan balance at the EOY 2?

e. What would be the monthly payments in year 1 if they are to be interest only?

f. Assuming terms in (e), what would monthly interest only payments be in year 2?

Answer 1

Please round off your answers as per your requirement.

Part (a)

An Adjustable Rate Mortgage (ARM) is made for $300,000 at an initial interest rate of 2 percent for 30 years.

Hence, PV of loan = - $ 300,000

Interest rate = 2% per annum

Frequency = monthly

Hence, interest rate per period = interest rate per month = 2% / 12 = 0.1667%

Time period = nos. of months in 30 years = 12 x 30 = 360

Hence, monthly payment can be calculated using PMT function in excel.

Inputs for PMT function are: PMT(rate, period, PV)

Hence, monthly payment during year 1 = PMT(rate, period, PV) = PMT(0.1667%, 360, -300000) = $1,108.86

Part (b)

Total principal portion paid during the first year = total principal paid over 12 monthly periods can be calculated using CUMPRINC(Rate, period, PV, start period, end period, type) = CUMPRINC(0.1667%, 360, 300000, 1, 12, 0) =  (7,373.65)

Hence balance loan principal after year 1 = 300,000 - 7,373.65 = $ 292,626.35

Part (c)

For year 2,

Loan amount = PV = - $ 292,626.35

Interest rate = 3% per annum

Frequency = monthly

Hence, interest rate per period = interest rate per month = 3% / 12 = 0.125%

Time period = nos. of months in 29 years = 12 x 29 = 360

Hence, monthly payment can be calculated using PMT function in excel.

Inputs for PMT function are: PMT(rate, period, PV)

Hence, monthly payment during year 2 = PMT(rate, period, PV) = PMT(0.25%, 348, - 292626.35) = $1,260.03

Part (d)

Total principal portion paid during the second year = total principal paid over 12 monthly periods can be calculated using CUMPRINC(Rate, period, PV, start period, end period, type) = CUMPRINC(0.25%, 348, 292626.35, 1, 12, 0) =  (6,429.51)

Hence balance loan principal after year 2 = 292,626.35 - 6,429.51 = $ 286,196.84

Part (e)

Interest only monthly payment in year 1 = interest per month = 300,000 x 2% x 1 / 12 = $  500.00

Part (f)

Interest only monthly payment in year 2 = interest per month = 300,000 x 3% x 1 / 12 = $ 750.00