You find that the going rate for a home mortgage with a term of 30 years is 6.5% APR. The lending agency says that based on your income, your monthly payment can be at most $750. How much can you borrow?
P = Po*r*t/(1-(1+r)^-t).
r = 0.065/12mo. = 0.00542/mo. = Monthly % rate.
P = 750/mo. * 360mo. = $270,000.
P = (Po*0.00542*360)/(1-1.00542^-360) = 270,000,
(Po*1.950)/0.8571 = 270,000,
2.275Po = 270,000, Po = $118,675.38.
To calculate how much you can borrow with a given monthly payment, you need to use the formula for calculating the monthly mortgage payment:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Where:
M = monthly payment
P = loan amount
i = monthly interest rate (APR / 12)
n = total number of payments (term in years multiplied by 12)
Let's calculate the loan amount (P) using the information provided:
Given:
APR = 6.5% (annual percentage rate)
Term = 30 years
Monthly payment (M) = $750
Step 1: Convert APR into a monthly interest rate:
i = APR / 12 / 100
= 6.5% / 12 / 100
= 0.0054167
Step 2: Calculate the total number of payments:
n = Term in years * 12
= 30 years * 12
= 360
Now, we can rearrange the formula to solve for the loan amount (P):
P = M [ (1 + i)^n - 1 ] / [ i(1 + i)^n ]
P = $750 [ (1 + 0.0054167)^360 - 1 ] / [ 0.0054167(1 + 0.0054167)^360 ]
By substituting the values into the formula and performing the calculation, you can find the loan amount (P) you can borrow with a maximum monthly payment of $750.