You are considering buying a new house, and have found that a $200,000, 30-year

Question

You are considering buying a new house, and have found that a $200,000, 30-year fixed-rate mortgage is available with an interest rate of 4 percent. This mortgage requires 360 monthly payments of approximately $947 each. If the interest rate rises to 5 percent, what will happen to your monthly payment?

Instruction: Round to the nearest dollar

The monthly payment will be $.  

Instruction: Round to the nearest tenth of a percent.

The change in the monthly payment will be  percent while the change in the interest rate will be  percent.

Explanation / Answer

Monthly payments of a loan can be calculated by the following formula -

M = P * ( J / (1 - (1 + J)-N))

Where

M = payment amount

P = principal, meaning the amount of money borrowed

J = effective interest rate

N = total number of payments

Here J = .05 / 12 = .00417

N = 360

P = $200,000

(1 + J) = 1.00417

(1 + J)- 360 = 0.22356

1 - (1 + J)- 360 = 0.77644

J / (1 - (1 + J)- 360) = 0.00537

P * [J / (1 - (1 + J)- 360) ] = $1074

If interest rate rises to 5% then monthly payment will be $1074.

The change in the monthly payment will be [{($1074 - $947) / $947} * 100] = 13.4 percent while the change in the interest rate will be [{(5 - 4) / 4} * 100] = 25 percent.

If we dont approximate then

Here J = .05 / 12 = .0041666667

N = 360

P = $200,000

(1 + J) = 1.0041666667

(1 + J)- 360 = 0.2238265956

1 - (1 + J)- 360 = 0.7761734044

J / (1 - (1 + J)- 360) = 0.0053682163

P * [J / (1 - (1 + J)- 360) ] = $1073.64326

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