# Suppose your gross monthly income is $5,200 and your current monthly payments are $625. If the bank will allow you to pay up to 36% of gross monthly income (less current monthly payments) for a monthly house payment, what is the maximum loan you can obtain if the rate for a 30-year mortgage is 4.65%? (Round your answer to the nearest cent.

## Allowable monthly payment

= 5200*.36 - 625 = 1247

Present value of possible mortgage:

i = .0465/12 = .003875

n = 30*12 = 360

PV = 1247(1 - 1.003875^-360)/.003875

= .....

## To find the maximum loan you can obtain, you need to calculate 36% of your gross monthly income (less current monthly payments) and then determine the maximum monthly house payment you can afford. Finally, you can use the affordability calculation to determine the maximum loan amount.

Step 1: Calculate 36% of gross monthly income (less current monthly payments):

Gross monthly income (less current monthly payments) = $5,200 - $625 = $4,575

36% of gross monthly income = 36% * $4,575 = $1,647

Step 2: Determine the maximum monthly house payment you can afford.

Maximum monthly house payment = $1,647

Step 3: Use the affordability calculation to find the maximum loan amount.

Let P be the maximum loan amount.

Using the loan affordability formula: P = (A / R) * (1 - (1 + R)^(-n))

Where A is the maximum monthly house payment, R is the monthly interest rate, and n is the total number of months.

In this case:

A = $1,647

R = 4.65% / 100 = 0.0465 (convert the interest rate to a decimal)

n = 30 years * 12 months/year = 360 months

Plugging the values into the formula: P = ($1,647 / 0.0465) * (1 - (1 + 0.0465)^(-360))

P ≈ $355,102.54

Therefore, the maximum loan you can obtain is approximately $355,102.54.

## To find the maximum loan you can obtain, we need to calculate the maximum monthly house payment you can afford based on the bank's requirements, and then use that to determine the loan amount.

Step 1: Calculate the maximum monthly house payment.

First, we need to determine 36% of your gross monthly income, excluding your current monthly payments.

Monthly Gross Income = $5,200

Current Monthly Payments = $625

36% of Gross Monthly Income = 36/100 * ($5,200 - $625)

= 36/100 * ($4,575)

= $1,647

So, the maximum monthly house payment you can afford is $1,647.

Step 2: Calculate the loan amount.

Once we know the maximum monthly house payment, we can use a mortgage calculator to determine the loan amount.

Using a mortgage calculator with a loan term of 30 years (360 months) and an interest rate of 4.65%, we can find the loan amount. We'll use the formula for the monthly payment on a fixed-rate mortgage:

M = P * (r(1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly Payment

P = Principal Loan Amount

r = Monthly Interest Rate (annual rate divided by 12)

n = Total Number of Payments (loan term in months)

Let's rearrange the formula to solve for the loan amount (P):

P = M * ((1 + r)^n - 1) / (r(1 + r)^n)

Now, substitute the given values:

M = $1,647

r = 4.65% / 100 / 12 = 0.003875

n = 360

P = $1,647 * ((1 + 0.003875)^360 - 1) / (0.003875(1 + 0.003875)^360)

Using a calculator, evaluate this expression:

P ≈ $300,972.12 (rounded to the nearest cent)

Therefore, the maximum loan you can obtain, given the given conditions, is approximately $300,972.12.