Question

John is considering an adjustable rate mortgage loan with the following characteristics:

• Loan amount: $400,000

• Term: 30 years

• Index: one year T-Bill

• Margin: 2%

• Periodic cap: 2%

• Lifetime cap: none

• Negative amortization: not allowed

• Financing costs: 1% origination fee and 2 points.  

The Treasury bill yield is 4% at the outset and is expected to increase to 6% at the beginning of the second year and to 11% at the beginning of the third year. If John pays off the loan at the end of the third year, what is the ARM’s effective borrowing cost?  

PART A- What is the monthly payment during the second year?  

a. $ 2,398.20

b. $ 2,923.44

c. $3,476.22

d. $4,523.68

e. None of the above

PART B- What is the loan balance at the end of the third year? a. $388,796

b. $389,268

c. $389,997

d. $392,985

e. None of the above

PART C- What is the effective borrowing cost? a. 9.62%

b. 9.81%

c. 9.89%

d. 9.03%

e. 9.60%

Answer 1

Given,

Index for 1^st year=4%, second year= 6% and for 3^rd year=11%

Margin= 2%

Periodic cap= 2%   Life time cap: None

Interest rates are as follows:

1^st year: 4% + 2% = 6%

2^nd year: 6% + 2% = 8%

3^rd year: 11% + 2% = 13% or previous rate of 8% plus cap of 2% =10% whichever is lower. Hence, the rate applied is 10%.

Also given,

Loan amount= $400,000. Origination fees= 1% Discount points=2

Therefore, net amount received on closing= Loan*(1-3)% = 400000*(1-3)%= $388,000

Part A: Monthly payments during the second year= $ 2,923.44

Answer is choice b

Part B: Loan balance at the end of the third year = $388,796

Answer is choice (a)

Effective borrowing cost= 9.03%

Answer is choice (d)

Calculation as below: