You have a $250,000 mortgage. The 30- year fixed rate is 8.5%. You have had your house for ten years. You have 20 years remaining on your mortgage. The new 15-year mortgage rate is 5.5%.
1) What is your mortgage payment, principal and interest on your current mortgage?
2) What would your new mortgage payment, principal and interest be if you refinanced?
3) What is your monthly savings?
4) Since you only had 20 years remaining on your 30-year mortgage, what would the total amount that you would pay out if you kept your current mortgage?
5) If you chose the new 15-year mortgage, what would be the total amount that you would pay out over the 15 years?
6) Why did you save so much with the 15-year mortgage?
Sorry,that it's long I really don't understand it!
No problem! I'll break it down step-by-step for you. To answer each of the questions, we will need to use some mortgage calculations formulas. Let's start with the first question:
1) To calculate your mortgage payment, principal, and interest on your current mortgage, we need to use the formula for an amortizing loan. The formula is:
P = (r * A) / (1 - (1 + r)^(-n))
P = monthly payment
A = loan amount
r = monthly interest rate (annual interest rate divided by 12)
n = total number of payments (30 years * 12 months per year - 10 years * 12 months per year)
Plugging in the given values:
A = $250,000
r = 8.5% / 100 / 12 = 0.0070833 (monthly interest rate)
n = (30 - 10) * 12 = 240 (number of payments remaining)
Calculating P using the formula:
P = (0.0070833 * $250,000) / (1 - (1 + 0.0070833)^(-240))
Your monthly payment, including principal and interest, on your current mortgage is the result of this calculation.
2) To calculate your new mortgage payment, principal, and interest if you refinanced to a 15-year mortgage, we will use the same formula as before, with some modifications. The formula becomes:
P = (r * A) / (1 - (1 + r)^(-n))
P = monthly payment
A = loan amount (same as before, $250,000)
r = monthly interest rate (annual interest rate for the new mortgage divided by 12)
n = total number of payments (15 years * 12 months per year)
Plugging in the given values:
r = 5.5% / 100 / 12 = 0.0045833 (monthly interest rate)
n = 15 * 12 = 180 (number of payments)
Calculating P using the formula will give us the new monthly payment, including principal and interest, if you refinance.
3) To calculate your monthly savings, subtract the new mortgage payment from the current mortgage payment. This will give you the difference in monthly payments.
4) To calculate the total amount that you would pay out if you kept your current mortgage, multiply your current monthly payment by the total number of payments remaining (240).
5) To calculate the total amount that you would pay out over the 15 years if you chose the new 15-year mortgage, multiply the new monthly payment by the total number of payments (180).
6) You would save money with the 15-year mortgage because the interest rate is lower (5.5% compared to 8.5%), and you would be paying off the loan in a shorter time. This means you would pay less interest over the life of the loan, resulting in overall savings.
Remember, these calculations are approximate, and there may be additional costs associated with refinancing your mortgage. It's always a good idea to consult with a financial advisor or mortgage specialist to get an accurate understanding of your specific situation.
No problem! I can help break it down for you step-by-step. Let's answer your questions one by one:
1) To calculate your mortgage payment, principal, and interest on your current mortgage, we need to use a mortgage payment formula. The formula is:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P = Monthly payment
A = Loan amount ($250,000)
r = Monthly interest rate (8.5% / 12 = 0.085 / 12)
n = Total number of payments (30 years * 12 = 360 payments)
Plugging in the values, we get:
P = (0.085/12 * $250,000) / (1 - (1 + 0.085/12)^(-360))
P ≈ $1,924.15
So, your current mortgage payment, principal, and interest is approximately $1,924.15.
2) Now, let's calculate your new mortgage payment, principal, and interest if you refinanced to the 15-year mortgage. We'll use the same formula as before, but with a different interest rate and number of payments.
r = Monthly interest rate of the new mortgage (5.5% / 12 = 0.055 / 12)
n = Total number of payments for the new mortgage (15 years * 12 = 180 payments)
Plugging in the values, we get:
P = (0.055/12 * $250,000) / (1 - (1 + 0.055/12)^(-180))
P ≈ $2,113.37
So, your new mortgage payment, principal, and interest would be approximately $2,113.37.
3) To find your monthly savings, subtract your new mortgage payment from your current mortgage payment:
Monthly savings = Current mortgage payment - New mortgage payment
Monthly savings ≈ $1,924.15 - $2,113.37
Monthly savings ≈ -$189.22 (Negative value means an increase in payment)
So, if you refinanced to the 15-year mortgage, you would have a monthly increase of approximately $189.22.
4) To calculate the total amount that you would pay out if you kept your current mortgage, multiply your current mortgage payment by the total number of payments:
Total amount paid = Current mortgage payment * Total number of payments
Total amount paid ≈ $1,924.15 * 360
Total amount paid ≈ $692,694.00
So, if you kept your current mortgage, you would pay out approximately $692,694.00 over the remaining 20 years.
5) To calculate the total amount that you would pay out over the 15 years if you chose the new 15-year mortgage, multiply your new mortgage payment by the total number of payments:
Total amount paid = New mortgage payment * Total number of payments
Total amount paid ≈ $2,113.37 * 180
Total amount paid ≈ $380,806.60
So, if you chose the new 15-year mortgage, you would pay out approximately $380,806.60 over the 15 years.
6) The reason you save so much with the 15-year mortgage is because the interest rate is lower. By refinancing to a lower interest rate, the interest portion of your monthly payment decreases, which leads to lower total interest paid over the life of the loan. Additionally, the term is shorter, so you pay off the loan faster and save on interest charges.
I hope this clarifies things for you! Let me know if you have any further questions.