Answer:
$294,815
Step-by-step explanation:
The relevant formula to use to calculate the largest mortgage loan the Prof. Business could qualify for is loan amortization formula.
Loan amortization is the spread of a loan into a number of fixed payments to be made over a specified period. The loan amortization formula is as follows:
P = {A × [r(1 + r)^n]} ÷ {[(1+r)^n]-1} .................................... (1)
Where,
P = Monthly required payment = $1,400
A = Mortgage loan amount = ?
r = interest rate = 4% per year = 0.04 pear year
= (0.04 ÷ 12) per month = 0.0033 per month
n = number of payment period = 30 years = (30 × 12) months = 360 months
If we substitute the figures above into equation (1), we will have:
1,400 = {A × [0.0033(1 + 0.0033)^360]} ÷ {[(1+0.0033)^360] - 1}
1,400 = {A × [0.0033(1.0033)^360]} ÷ {[(1.0033)^360] - 1}
1,400 = {A × [0.0033 × 3.2741]} ÷ {3.27410 - 1}
1,400 = {A × 0.0108} ÷ 2.2741
We can now rearrange and solve for A as follows:
A × 0.0108 = 1,400 × 2.2741
A × 0.0108 = 3,184
A = 3,184 ÷ 0.0108
A = 294,815
Therefore, the largest mortgage loan the Prof. Business could qualify for is approximately $294,815.