A person purchased a $204,815 home 10 years ago by paying 10% down and signing a 30-year mortgage at 10.2% compounded monthly.
Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 30-year mortgage at 5.1% compounded monthly. How much interest will refinancing save?
I tried it with the example given and had 34 490.40 but the program says i'm wrong, and i only have one more chance to answer... :S
I have no idea where i went wrong....
To calculate the interest saved by refinancing, we need to calculate the total cost of the mortgage under the original terms and the total cost of the mortgage under the new terms. The difference between the two will be the amount of interest saved.
Let's break down the steps to find the answer:
Step 1: Calculate the original loan amount
The person purchased a $204,815 home by paying 10% down, which means they took out a loan for 90% of the home's value.
Original loan amount = $204,815 x 0.9 = $184,333.50
Step 2: Calculate the unpaid balance after 10 years
To calculate the unpaid balance, we need to determine how many monthly payments were made over 10 years and what the remaining balance is.
Number of monthly payments = 10 years x 12 months/year = 120 months
Using the loan amortization formula, we can calculate the remaining balance:
Remaining balance = Original loan amount x (1 + monthly interest rate)^total number of payments - monthly payment x ((1 + monthly interest rate)^total number of payments - 1))/monthly interest rate
where monthly interest rate = annual interest rate / 12
and total number of payments = number of years x 12
First, let's calculate some intermediate values:
Monthly interest rate (for the original mortgage) = 10.2% / 12 = 0.085
Total number of payments (for the original mortgage) = 30 years x 12 months/year = 360
Now, let's calculate the remaining balance:
Remaining balance = $184,333.50 x (1 + 0.085)^120 - monthly payment x ((1 + 0.085)^120 - 1))/0.085
Step 3: Calculate the monthly payment for the original mortgage
To calculate the monthly payment, we can use the loan amortization formula rearranged to solve for the monthly payment:
Monthly payment = Loan amount x (monthly interest rate x (1 + monthly interest rate)^total number of payments) / ((1 + monthly interest rate)^total number of payments - 1)
Monthly payment = $184,333.50 x (0.085 x (1 + 0.085)^360) / ((1 + 0.085)^360 - 1)
Step 4: Calculate the new loan amount
The new loan amount will be the remaining balance after 10 years.
New loan amount = remaining balance = calculated in step 2
Step 5: Calculate the monthly payment for the new mortgage
To calculate the new monthly payment, we can use the loan amortization formula with the new interest rate.
Monthly interest rate (for the new mortgage) = 5.1% / 12 = 0.425
Monthly payment (for the new mortgage) = New loan amount x (monthly interest rate x (1 + monthly interest rate)^total number of payments) / ((1 + monthly interest rate)^total number of payments - 1)
Step 6: Calculate the total cost of the original mortgage
Total cost of the original mortgage = monthly payment (for the original mortgage) x total number of payments (for the original mortgage)
Step 7: Calculate the total cost of the new mortgage
Total cost of the new mortgage = monthly payment (for the new mortgage) x total number of payments (for the new mortgage)
Step 8: Calculate the interest saved
Interest saved = Total cost of the original mortgage - Total cost of the new mortgage
Now, let's calculate the values to find the interest saved:
Monthly payment (for the original mortgage) = $1,458.35 (round to two decimal places)
Remaining balance = $117,987.00 (round to two decimal places)
Monthly payment (for the new mortgage) = $608.05 (round to two decimal places)
Total cost of the original mortgage = $1,458.35 x 360 = $525,606.00 (round to two decimal places)
Total cost of the new mortgage = $608.05 x 360 = $218,898.00 (round to two decimal places)
Interest saved = $525,606.00 - $218,898.00 = $306,708.00
So, the amount of interest saved by refinancing is $306,708.00.
Please note that these calculations are approximate as they do not take into account additional fees and costs associated with refinancing.