Colli Real Estate

Calculate the amount of the monthly payment?

On December 31, 1995, a house is purchased with the buyer taking out a 30-year
$90, 000 mortgage at 9% interest compounded monthly. The mortgage payments are made at the end of each month. Calculate the amount of the monthly payment

30
90000
0.09
12
=(1+a3/a4)^(a1*a4)
=a5/(a5-1)
=a6*a2*a3/a4

30
90000
0.09
12
14.73057612
1.072830156
724.1603553

I make it $724.16 per month

The formula is MP = i * PA * (1+i)^n /(((1+i)^n) – 1), where MP = monthly payment, i = monthly effective interest rate, PA = principal amount, and n = number of compounding periods – namely, months.

In case you are interested in the source of this formula, it derives from the mathematical formula for the sum of a geometric series: S = 1 + x + x^2 + x^3 + … + x^(n-1) = (x^n – 1) / (x – 1). Now, you can verify this, by multiplying the series S by (x – 1) and seeing that, because of some very convenient cancellation, you get x^n – 1.

Now, by letting x = 1 + i, you have the amount to which a monthly deposit of $1.00, made at the end of the month, accumulates, with interest, at the end of n years: namely,
S = (((1 + 1)^n) – 1) / i.

Now, if you divide this by (1 + i)^n, you get the present value of this accumulation: namely,
a = ((1 + i)^n – 1) / (i (1 + i)^n).

To get ‘ i ‘, the monthly effective rate, I divided .09 by 12, since the 9% was already given as being compounded monthly. To get the monthly payment, then, I divided PA by a. You can see, from the numbers cryptically shown at the top, that I used Excel to do the calculation.

I hope this helps you out.

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