Formula To Calculate Mortgage Payment
I have some problems on calculate the mortgage monthly
payment(capital +interest).
My cases is
Capital: 54600 pounds
Interest rate:8.45%
Tax relief on first 30000 pounds is 15%
Term is 20 years
1. The formula to calculate the monthly payment include the tax relief
2. If I have discount rate of 6.95% for 2 years, How to calculate the
monthly payment including tax relief
3. If I have fixed rate of 7.70% for 5 years, how to calcualte the
monthly payment including tax relief
1/There is no formula to take into account tax relief, you have to guess and
simulate until you get the debt down to zero after 20 years. The reason
for this is that the standard formula, which is P = C*r/(1-(1+r)^-n)
(where P is the payment per period, C is the capital, r is the interest
rate per period and n is the number of periods), only works when the
interest rate is constant. With tax relief the effective interest rate
decreases over the loan term because the debt reduces. At the beginning
the effective interest rate is (k*30000+C-30000)*r/C, and as soon
as the debt drops below 30000 the effective interest rate becomes k*r,
where k = 0.9 for 10% relief (or k=0.85 for 15% relief).
If your lender uses monthly reconciliation, then the r in the formula
should be the monthly interest rate and n should be the number of months.
I can tell you that the answer is 452.59 because I have a program to do
the simulation I mentioned. But let's see what answer you get if you
use the simple formula using the initial effective rate.
First calculate the effective rate: (0.9*30000+24600)*8.45%/54600 = 7.9857%,
This makes the monthly rate 0.66548%. So the formula you want is:
P = 54600*0.0066548/(1-1.0066548^-240) which gives the answer 456.21.
That's pretty close to the correct answer. Now, if your lender operates
annual instead of monthly reconciliation, then instead you want the formula
P = 54600*0.079857/((1-1.079857^-20)*12), which gives 462.93.
2-3/ The answer depends on how the lenders calculate it. They probably will
calculate the amounts payable for the discount period as if the discounted
rate applied for the whole 20 years. So just use the same formula.
Assuming monthly reconciliation, and 10% relief, the true answers are
406.00 for 6.95% and 428.97 for 7.70%, and the corresponding approximate
answers are 409.28 and 432.44.
But what you also want to know is what the payments will be after the
discount periods are over. What you need to do here is work out by
how much the debt has gone down during the period, and then do a new
calculation using the new interest rate, the new debt, and a new period
of 18 or 15 years.