The Project’s Situation, Statistics Problem Example

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Statistics problem

Problem: Assuming you have a surplus one hundred dollars each month, can you pay off your twenty-five year mortgage in twenty years? The mortgage was taken out five years ago. If the mortgage is refinanced, what is the highest interest rate that you can afford to pay to meet the twenty year goal?

Approach: The first step is to calculate the maximum payment that can be made each month. This could be done simply by adding the extra money to the current monthly payment. Then I will calculate the whether or not this will be sufficient at the current interest rate. To do this, it will be necessary to figure out the amount that must be paid each month and then compare this maximum payment total to the minimum required payment. If the maximum payment you can make exceeds or is equal to the minimum required payment, it will be advisable to try and make the payment in twenty years. After concluding this analysis, the idea of refinancing will be examined. To do this, the maximum interest rate must be calculated. To find the maximum interest rates and monthly required payments, a mortgage payment formula will be used.

Conclusion: The initial payment needed each month is $706.12 before the additional money that needs to be added to the escrow account is included. Reducing the length of the loan by five years would require a monthly payment of over 932 dollars a month. This is significantly over the maximum payment that can be made each month ($806.12), therefore at this interest rate, this cannot be done. If the interest rate can be lowered through refinancing, it may become feasible to pay the loan off in the twenty year period. The maximum interest payment in which the mortgage can be paid off in the shorter period is approximately 3.55.

Solution Details:

formula for mortgage payments

This is the formula for mortgage payments, expressed by the outstanding amount borrowed. It can be reexpressed in terms of A, the monthly payment as such.

monthly payment

A is the monthly payment, P is the amount outstanding, r is the interest rate per month, and n is the periods left on loan. (In the case of a monthly payment, this will equal twelve times the number of years.) In this specific case, we have this.

specific case

A=932.12.

This equation could be reexpressed in terms of interest rate; however that would require great deals of algebra. Since I had already entered the formula into Microsoft Excel, it was easier to run guess and check until the required payment was equal to the possible payment. The equation in which this takes place is as follows.

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