Question

Consider a FA 30yr LPM 3/1 ARM with no interest rate caps and no payment caps. The loan is for $200,000, with two points and other Regulation-Z fees of $3,000. The fixed period rate is 4% and the margin 2.5%. The underlying index at dates 0,1,2,3,4,5,6 years is 2%, 2.5%, 3%, 3.5%, 4%, 4%, 5%, respectively, and then stays at 5.5% until mortgage maturity.

What is the APR?

Answer 1

Given FA (fully amortized) 30 Year LPM (Level Payment Mortgage) has 3/1 ARM with no interest rate caps and payment caps.

Here we understand that 3/1 adjustable rate mortgage is a product that carries fixed interest amount for first three years (4% + 2% margin) and for the rest of the 27 years we shall consider the variable interest rates as provided in the problem.

Given Loan is around $200000, with one time fee of $3000 for Regulation Z and two points on the loan(buying down).

We calculate two points on $200000 such as by dividing the total loan amount by 2%(each point is equal to one percent of the total loan). We get $4000.

We'll calculate Monthly Payments for first three years with the fixed interest rate and margin rate i.e., 6.5 percent. Rest of the years as in mentioned interest rate added with margin interest rate.

Monthly Payment Formula is P{r(1+r)^n/(1+r)^n-1 whereas P is Principal, r is monthly interest rate and n is number of months.

To calculate easily on Excel spreadsheet, the required formula is =PMT(Interest rate/Payments per year, Total Number of Payments, Loan Amount, 0)

Total monthly payments is $41641.

Calculating APR using below formula :

[{(Fees+Interest Paid / Loan Amount)/Number of Days in Loan Term}×365]×100

In Excel the formula is =Rate(Loan Term in Months,Total Monthly payments,(Principal Amount - Two Points-Regulation Z Fees)×12)

Substituting values we get APR(Annual Percentage Rate) of 1.79% , rounding off 2%.