## What’s the Cost of My Mortgage

Business Application: What’s the Cost of My Mortgage? The loan department of your bank still uses silly tables to determine what the monthly payment of a mortgage loan is going to be. The consumer association wants you to design a program to compute interactively monthly mortgage payments as well as the cost of such a annual loan over the first 5 years of the loan, and the total cost of that loan. In order to validate the input data, the annual loan amounts must be between \$1,000 and \$500,000, the loan interest must be between 3 and 20%, and the loan length must always be between 1 and 35 years. First, we must compute the monthly payment. To see how this can be done, let’s start with a simple example and build up to the general case. Suppose a loan of \$1000 made at an interest rate of 10%. If there is to be a single payment P at the end of the load period then If the repayment were to be made in two equal payments of P spaced at equal intervals and the interest rate for each of the periods were 5%, then P must be such that

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