Mortgage payment/Compound interest? Pz help?

X financed $53,492.92 on a 10% fixed rate mortgage payable monthly over 30 years. What is his monthly payment? Plz show calculations

Mortgage payment/Compound interest? Pz help?

I am going to introduce a term called present value. Basiclaly if I have a payment of Y dollars coming up in 15 months the present value is the amount of dollars you would have to pay now to not have to Pay the Y dollars 15 months from now.

Now comes the fun part. The combined present value of all those payments you make on the above mortgage is going to be worth the amount financed. Say X is your monthly payment.

I am going to assume that this mortgage is compounded monthly so a 10 percent rate for the year is a .83333...% a month loan.

Now call Pi the present value of the payment made at the end of month i. Pi*(1.0083333...)^i=X

So Pi=X*(1.0083333...)^(-I)

Now we have the sum of Pi for i =1 to 360 needs to be 53492.92 This is the sum of a geometric series so we have

53492.92= X*( (1.0083333...)^0- (1.0083333...)^(-360) / ((1.0083333...)-1)

Or 53492.92=X*113.951

Thus we have X=469.44

Mortgage payment/Compound interest? Pz help?

The general equation for payments at a fixed interest rate is:

payment = (principle+r) / (( 1.0-(1.0 + r)^n), where principle is the amount of the load, $53,392.92 in this case. r is the interest rate per period and n is the number of periods. The

catch here is the payment rate is monthly on the rate per period is 10%/12 = .10/12 = ,0083333, and the number of periods is 12(months/year_ * 30 years = 360 periods, so the

equation is

payments = $53,392.92 *0.008333..)/(1- (1.0+.0083333)^360)

payments = $469.44

Mortgage payment/Compound interest? Pz help?

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