Find the total amount paid on a 30-year mortgage for $53,000 with an interest rate of 4.25%.
P = Po*r*T/(1-(1+r)^-T),
r = 0.0425/12 = 0.00354 = Monthly % rate.
T = 30yrs * 12mo./yr. = 360 months.
P = (53,000*0.0425*360)/(1-1.00354^(-360)) = $93,839.79.
To find the total amount paid on a 30-year mortgage, we need to calculate the total loan payments (including both principal and interest) over the course of 30 years. Here's how you can calculate it step by step:
Step 1: Calculate the monthly interest rate
Divide the annual interest rate by 12 to get the monthly interest rate.
Monthly interest rate = (Annual interest rate) / 12 = 4.25% / 12 = 0.0425 / 12 = 0.0035417 (rounded to 6 decimal places)
Step 2: Calculate the number of months
Multiply the number of years (30) by 12 to get the total number of months.
Number of months = 30 years * 12 = 360 months
Step 3: Calculate the monthly payment
To calculate the monthly payment, we can use the formula for calculating the monthly mortgage payment:
M = P * [r(1+r)^n] / [(1+r)^n-1]
Where:
M = Monthly payment
P = Principal (loan amount)
r = Monthly interest rate
n = Number of months
M = 53000 * [0.0035417(1+0.0035417)^360] / [(1+0.0035417)^360-1]
Using this formula, we can find the monthly payment amount.
Step 4: Calculate the total amount paid
Multiply the monthly payment by the total number of months.
Total amount paid = Monthly payment * Number of months
Now, let's calculate the total amount paid:
Monthly payment = 53000 * [0.0035417(1+0.0035417)^360] / [(1+0.0035417)^360-1] ≈ $253.76 (rounded to 2 decimal places)
Total amount paid = Monthly payment * Number of months
Total amount paid = $253.76 * 360 = $91,353.60
So, the total amount paid on a 30-year mortgage for $53,000 with an interest rate of 4.25% would be approximately $91,353.60.