Professor Christine Curley
Technology is pervading all levels of mathematics teaching and learning in our modern world, bringing ever more sharply into focus the change from traditional pencil and paper learning to a mixture of calculator, computer and pencil and paper learning environments. Currently the loan has 25 years remaining. Therefore to find out the P&I payment, you would plug in 300 for N (25x12), 5.75% for I, 0 for FV, and $112,242.47 for PV, and then press PMT which gives you the $706.12. However, we want to find out how much more money they have to pay to pay off the loan in 20 years instead of 25. Therefore change N to 240 (20x12) instead of 300. Then press PMT and we should get $788.04. Next, subtract the P&I payment they are making now (706.12) from $788.04, which tells you they need to pay $81.92 extra towards the principal each month to have the loan paid off in 20 years instead of 25. This may be reasonable. $81.92 is pretty close to $100 so there really isn’t a lot of wiggle room after meeting the monthly expenses. However, it’s important to note that if you do this way (instead of refinancing), you are not obligated to pay this $81.92 each month if you needed it for something else. Since refinancing costs you $2,000 up-front, we’ll have to add this to the payoff of 112,242.47. This would cause the PV of the loan to be 114,242.47. The new loan would be based on the 30 years, so plug 360 in for N. FV will still be 0. In order to find the highest interest rate you can qualify for that still gives you a P&I payment less than your current payment, let’s put in a payment of $706.11 (one penny less than the current payment). This gives us a maximum interest rate of 6.29%....