IF i AM PAYING $1,626.83 MONTH FOR 15 YEARS AT 4% WHAT WOULD THE ORIGINAL MORTGAGE AMT BE
P=1626.83 * 15yrs. * 12mo./yr.=292829.40
P = (Po*r*t)/(1-(1+r)^-t) = 292829.40
r = (4%/12)/100% = 0.00333 = Monthly % rate expressed as a decimal.
t = 15yrs. * 12mo/yr. = 189 Months.
(Po*0.00333*180)/(1-(1.00333)^-180)=
292,829.40
0.5994Po/0.45031 = 292829.40
1.33108Po = 292829.40
Po = $ 219,993.84
Correction: t = 180 Months.
To calculate the original mortgage amount, you can use the formula for calculating the monthly mortgage payment:
M = P * (r(1+r)^n)/((1+r)^n-1)
Where:
M = monthly mortgage payment
P = principal amount (original mortgage amount)
r = monthly interest rate (annual interest rate / 12)
n = total number of monthly payments (number of years * 12)
In this case, you know the monthly payment amount ($1,626.83), the interest rate (4%), and the loan term (15 years).
Step 1: Convert the annual interest rate to a monthly rate:
r = 4% / 12 = 0.0033333
Step 2: Calculate the total number of monthly payments:
n = 15 years * 12 = 180 months
Step 3: Rearrange the formula to solve for the principal amount (P):
P = M * ((1+r)^n-1) / (r(1+r)^n)
Plug in the known values:
P = $1,626.83 * ((1+0.0033333)^180-1) / (0.0033333(1+0.0033333)^180)
Now, you can calculate the original mortgage amount by solving this equation. The result will give you the principal amount you borrowed initially.