Many mortgage lenders offer the flexibility of dividing a mortgage loan between a fixed-interest-rate portion and a variable-interest-rate portion. (A variable-rate mortgage is sometimes referred to as an adjustable-rate mortgage, abbreviated ARM.) The variable interest rate changes from time to time, following the trend of short-term interest rates in the capital markets. On average, quoted variable interest rates on mortgages are lower than quoted fixed rates for most terms. But at times variable rates can rise above (even substantially above) fixed rates, especially fixed rates that may have been “locked in” two or three years earlier.
Suppose a $100,000 mortgage loan with a 25-year amortization is divided equally between a fixed-rate portion at 6.6% compounded semiannually and a variable-rate portion at 5.4% compounded monthly. (Quoted rates on variable-rate mortgages are normally monthly compounded rates.)
a. What is the initial (combined) monthly payment?
b. What will be the combined monthly payment if the variable rate jumps to 6.6% compounded monthly after two years?