How to calculate mortgage loan instalments?

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There exists many automated tools for the calculation of mortage loan such as this website.
However, I believe having a detailed mathematical understanding for the calculation of mortage payments is paramount as undeniably, this formula plays such a key role in the lives of many.
The formula is:
M = P [ i(1 + i) ^n ] / [ (1 + i)^n - 1]
To illustrate the working of this formula.

Say for a $100,000 mortgage at 5% compounded monthly for 15 years, we would first solve for i as

i = 0.05 / 12 = 0.004167 and
n as 12 x 15 = 180 monthly payments

Next we would solve for (1 + i)^n = (1.004167)^180 using the xy key on the calculator, which yields 2.11383

Now our formula reads M = P [ i(2.11383)] / [ 2.11383- 1] which simplifies to

M = P [.004167 x 2.11383] / 1.11383 or
M = $100,000 x 0.00791 = $791.81

Comments

Anonymous said…
I am curious if the mortgage rates r fixed for 15yrs ? Ours was fixed every 5yrs. During each term, a same amount is deducted monthly from our acount.

As more principal were paid off, the equation within this amount is more principal n less interest.

The bank did profit from 3 times the principal borrowed. We r allowed to deduct the interest paid via income tax(scale of 38% to 52%). Real estate is not a money maker here, so we cant recoup back the great expense.

I know that most buyers in Sg pay via CPF. Is there a provision for tax deduction for those who borrowed from the banks ?
Fri Jan 30, 05:27:00 AM GMT+8
Singapore Short Stories said…
Oh Dutchie, it was just an example. Usually for flats here in Singapore, its 20 years.

I am not too sure of the provision though.
Sat Jan 31, 11:30:00 AM GMT+8
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