Question

Suppose you wish to buy a house costing $200,000. You will put a down payment of 20% of the purchase price and borrow the rest from a bank for 30 years at a fixed rate r compounded monthly. If you wish your monthly mortgage payment to be $1,500 or less, what is the maximum annual interest rate for the mortgage loan?

If you could work out the steps that would be great. I am having trouble simplifying the equation and I was able to figure out the answer graphically but not sure if there is another way to do it.

Answer 1

Information provided:

Purchase price of the house= $200,000

Monthly mortgage= $1,500

Down payment= 0.20*$200,000= $40,000

Mortgage= $200,000 - $40,000= $160,000

Time= 30 years*12= 360 months

The question is solved by entering the below in a financial calculator:

PV= -160,000

N= 360

PMT= 1,500

Press the CPT key and I/Y to calculate the interest rate.

The value obtained is 0.9003.

Therefore, the maximum annual interest rate is 0.9003%*12= 10.80%.

In case of any query, kindly comment on the solution.