According tto baank lending rules, Prof. Business can afford a maximum monthly mortgage payment of $1,400 What is the largest mortgage loan the Prof. Business could qualify for if current 30-year mortgage rates are 4% APR?

$294,815

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.

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