A person purchased a $180477 home 10 years ago by paying 15% down and signing a 30-year mortgage at 9.3% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 20-year mortgage at 6% compounded monthly How much interest will refinancing save? Money Saved =?

Sure, let's break this down step by step.

Step 1: Calculate the initial mortgage amount The person paid 15% down on a $180,477 home. So, the initial mortgage amount is 85Initial Mortgage = 180477 * 0.85 =$153,405.45

Step 2: Calculate the monthly payment for the initial mortgage The initial mortgage was a 30-year (or 360 months) mortgage at 9.3% interest compounded monthly. We can use the formula for the monthly payment on a loan: M = P[r(1+r)^n]/[(1+r)^n – 1] where: M is your monthly payment. P is the principal loan amount. r is your monthly interest rate (annual interest rate of 9.3% divided by 12). n is number of payments (or the number of months in the term). So, M = 153405.45[(0.0093/12)(1+0.0093/12)^360]/[(1+0.0093/12)^360 – 1] M = $1236.38

Step 3: Calculate the total interest paid for the initial mortgage Total interest paid is simply the monthly payment times the number of payments, minus the initial loan amount. Total Interest = (M * n) - P Total Interest = (1236.38 * 360) - 153405.45 = $290,696.55

Step 4: Calculate the remaining balance after 10 years After 10 years (or 120 months), there is still 20 years (or 240 months) left on the mortgage. We can calculate the remaining balance using the formula: B = P[(1 + r)^n - (1 + r)^x] / [(1 + r)^n - 1] where: B is the remaining balance. P is the principal loan amount. r is your monthly interest rate. n is number of payments (or the number of months in the term). x is the number of payments made. So, B = 153405.45[(1 + 0.0093/12)^360 - (1 + 0.0093/12)^120] / [(1 + 0.0093/12)^360 - 1] B = $141,643.59

Step 5: Calculate the monthly payment for the new mortgage The new mortgage is a 20-year (or 240 months) mortgage at 6% interest compounded monthly. We can use the same formula as in step 2, but with the new values. M = 141643.59[(0.06/12)(1+0.06/12)^240]/[(1+0.06/12)^240 – 1] M = $1012.96

Step 6: Calculate the total interest paid for the new mortgage Total Interest = (M * n) - P Total Interest = (1012.96 * 240) - 141643.59 = $101,068.41

Step 7: Calculate the interest saved by refinancing Interest Saved = Total Interest (old mortgage) - Total Interest (new mortgage) Interest Saved = $290,696.55 -$101,068.41 = $189,628.14

So, refinancing the mortgage would save approximately $189,628.14 in interest.