Question

Beverly Frost bought a home for $190,000 with a down payment of $19,000 at 7% for 25 years. Since then the rate has risen to 9%. How much more would her monthly payment be if she bought the house at 9%?

Answer 1

We start by figuring out the present value of the remaining balance for the home, which is 190000 - 19000 = 171000.  We must also figure out the monthly interest rate, since the rate given does not say it is a nominal rate, nor does it say it is compounded monthly, so we assume that is is NOT a nominal rate.  Let's call them i7 and i9.  So i7 = (1.07^(1/12) - 1) = .00565415 and i9 = (1.09^(1/12) - 1) = .00720732.
Now we just have to figure out the monthly payment under both interest rates.  At 7%, we have 171000 = x * a angle 300
which becomes 171000 = x * (1 - 1.00565415^-300)/.00565415
So, the monthly payment, x7 is 1185.24.
At 9%, we have 171000 = x * a angle 300 (at the i9 rate)
which becomes 171000 = x * (1 - 1.00720732^-300)/.00720732
So, the monthly payment, x9 is 1394.13.
The difference between monthly payments would be 1394.13 - 1185.24 = 208.89, which is the final answer.