A $120,000 home mortgage for 30 years at 7% has a monthly payment of $839.06. Part of the monthly payment is paid toward the interest charge on the unpaid balance, and the remainder of the payment is used to reduce the principal. The amount that is paid toward the interest is: = ( 12) (1 + 12) 12 The amount that is paid toward the reduction of the principal is: = ( 12) (1 + 12) 12 In these formulas, P is the size of the mortgage, r is the interest rate, M is the monthly payment, and t is the time in years. If the repayment period was changed from thirty years to twenty years, the monthly payment would be $966.71.

The question: We can get an estimate of the time when the monthly payment is divided evenly between interest and principal reduction from the graph. To get a closer result we can solve by using techniques involving exponential equations. For this part of the project you need to set u and v equal and solve for the variable t. Use the values given in the situation for this mortgage loan. All work should be shown, and if necessary, round your results to three decimal places. You should do this for both the 30 year mortgage and the 20 year mortgage.