Final answer:
a. The monthly payment on the original 6.5% mortgage was approximately $1,326.27. b. The remaining balance after 10 years (the amount they then refinanced) was approximately $154,587.99. c. The total interest paid during the first 10 years was approximately $55,412.01. d. The monthly payment on the refinance 4.25% mortgage is approximately $764.63. e. The total interest paid over the 30 year term of the refinance is approximately $154,441.77. f. The total interest paid over the full 40 years the Jacksons have a loan for the house is approximately $209,853.78.
Step-by-step explanation:
a. To find the monthly payment on the original 6.5% mortgage, we can use the formula for calculating the monthly payment on a fixed-rate mortgage:
PMT = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = principal amount (loan amount) = $210,000
r = monthly interest rate = 6.5% / 12 = 0.0054167 (decimal)
n = total number of payments = 30 years * 12 months = 360
Plugging in these values into the formula, we get:
PMT = ($210,000 * 0.0054167 * (1 + 0.0054167)^360) / ((1 + 0.0054167)^360 - 1) = $1,326.27 (approx)
Therefore, the monthly payment on the original 6.5% mortgage was approximately $1,326.27.
b. The remaining balance after 10 years (the amount they then refinanced) can be calculated using the formula for the remaining balance on a mortgage:
B = P * ((1 + r)^n - (1 + r)^t) / ((1 + r)^n - 1)
Where:
B = remaining balance after t years
P = principal amount (loan amount) = $210,000
r = monthly interest rate = 6.5% / 12 = 0.0054167 (decimal)
n = total number of payments = 30 years * 12 months = 360
t = number of payments made = 10 years * 12 months = 120
Plugging in these values into the formula, we get:
B = $210,000 * ((1 + 0.0054167)^360 - (1 + 0.0054167)^120) / ((1 + 0.0054167)^360 - 1) = $154,587.99 (approx)
Therefore, the remaining balance after 10 years (the amount they then refinanced) was approximately $154,587.99.
c. The total interest paid during the first 10 years can be calculated by subtracting the remaining balance after 10 years from the original loan amount:
Total interest paid = Original loan amount - Remaining balance after 10 years = $210,000 - $154,587.99 = $55,412.01
Therefore, the total interest paid during the first 10 years was approximately $55,412.01.
d. To find the monthly payment on the refinance 4.25% mortgage, we can use the same formula as in part a, but with updated values:
P = remaining balance after 10 years = $154,587.99
r = monthly interest rate = 4.25% / 12 = 0.0035417 (decimal)
n = total number of payments = 30 years * 12 months = 360
Plugging in these values into the formula, we get:
PMT = ($154,587.99 * 0.0035417 * (1 + 0.0035417)^360) / ((1 + 0.0035417)^360 - 1) = $764.63 (approx)
Therefore, the monthly payment on the refinance 4.25% mortgage is approximately $764.63.
e. To find the total interest paid over the 30 year term of the refinance, we can multiply the monthly payment by the total number of payments and subtract the remaining balance:
Total interest paid = (Monthly payment * Number of payments) - Remaining balance = ($764.63 * 360) - $154,587.99 = $154,441.77 (approx)
Therefore, the total interest paid over the 30 year term of the refinance is approximately $154,441.77.
f. To find the total interest paid over the full 40 years, we can sum up the interest paid during the first 10 years and the interest paid over the 30 year term of the refinance:
Total interest paid = Interest paid during the first 10 years + Interest paid over the 30 year term of the refinance = $55,412.01 + $154,441.77 = $209,853.78 (approx)
Therefore, the total interest paid over the full 40 years the Jacksons have a loan for the house is approximately $209,853.78.