True or False?
You should have said false. If the fall in interest rates is accompanied by an equal fall in real interest rates, then the statement would be true. If the fall in interest rates is the result of a fall in the expected future inflation rate, real interest rates will remain unchanged and real mortgage payments will not decline along with the observed decline in nominal interest rates. People would have no additional incentive to purchase houses.
Some subtle arguments are often brought up to try to defend the frequently heard argument that a fall in interest rates will improve the housing market. One of these is the argument that the limits on the maximum amount a home buyer can borrow will not fall with a fall in inflation rates and interest rates, so that mortgages will become more affordable. This has to be a temporary phenomenon at best because it is not in the interest of mortgage lenders to lend on the basis of nominal instead of real values.