Question

You are considering an adjustable rate mortgage loan with the following characteristics:

• Loan amount: $300,000

• Term: 20 years

• Index: one year T-Bill

• Margin: 2.5%

• Periodic cap: 2%

• Lifetime cap: 5%

• Negative amortization: not allowed
• Financing costs: $3,500 in origination fees and 1 discount point

Suppose the Treasury bill yield is 3.5% at the outset and is then moves to 4.5% at the beginning of the second year and to 8.5% at the beginning of the third year.

a) Build a table that shows the contract rate, monthly payment, and the end-of-year balance for years 1-3.

b) If you pay off the loan at the end of the third year, what is your effective borrowing cost? (Don’t forget about the financing costs).

Answer 1

Index means here a benchmark rate on which adjustable rate mortgage is decided. This benchmark rate is variable. Here Yield on T-Bill is index here.

Margin means here is fixed interest rate, which is added to the benchmark interest rate. Thus, adjustable rate mortgage has two components benchmark rate which is variable and margin rate which is fixed.

Periodic cap means how much interest rate can increase at every resiving the interest rate.

Lifetime cap means that how much interest can increase during the life of loan

a.) for the first year interest rate will be T-bill + margin = 3.5% + 2.5% = 6%

Table for the first year:

Bal = Loan balance

Pri = Principal amount

int =interest amount

Emi =Equated monthly Installment

period column here numbers of month.

Loan balance at the end of 1st year is $ 292,676.51.

This is calculated by excel functions ("PMT" for EMI, "PPMT" for principal amount, "IPMT" for interest amount)

PMT

In rate we need to put interest rate. So here 6% and it is divided by 12 because we are paying monthly.

Nper is total number of period for loan repayment

PV is loan amount

After puting these values in PMT function we will get EMI.

In EMI principal and interest payment both are included. So for finding pricnipal payment we use PPMT function.

PPMT

Here in all arguments remains same as in PMT expect Per.

Per is period. So just write period for which you want to know or calculated principal payment. Here I write 1 for first month principal payment.

And for finding Interest amount use IPMT

Here all arguments remains same as in PPMT.

After this from loan amount minus principal amount which is paid in proceeding installments. To get the loan balance amount.

Now at the starting of 2nd year loan balance is $ 292,676.51 and in 2nd year interest rate is 7% (4.5% + 2.5%) and Nper is 240 -12 = 228 again by using excel function I have prepared the table for 2nd year. Loan balance at the end of 2nd year is $ 285,181.22.

Here by using same excel function it is prepared.

Now at the starting of 3rd year loan balance is $ 285,181.22 and interest rate is 9% ( interest can only be increase by upto 2% because of periodic cap) so this time interest rate increase by 2%), Nper is 228 - 12= 216 again by using excel function I have prepared the table for 3rd year.

Now at the end of 3rd year loan balance is $ 277,915.28

b.) If you pay off loan by the end of 3rd year. The effective borrowing cost wii be,

all interest payment + financing cost + pre closure chagres

Here 1 discount point is pre closure charges. It means 1% of loan amount

So total cost of borrowing is

17,782.12 (interest for 1st year) + 19,692.12 (interest for 2nd year) + 24090.20 (interest for 3rd year) + 3,500 (financing cost) + 3,000 (discount point)

= $ 68064.53

Effective rate = (total cost of borrowing * 100) / Loan amount * life of loan

= (68064.53 *100) / 300,000 * 3

= 7.56%

The effective rate of borrowing is 7.56%.