Your annual income is $50,000. You want to take out a mortgage loan to buy a house. The rule on mortgage loan requires that your annual mortgage payment cannot exceed 30% of your annual income. If the current interest rate is 5% for a 30-year mortgage loan, what is the maximum amount one can borrow for a house?

To figure out the maximum amount you can borrow for a house, we first need to calculate 30% of your annual income.

Step 1: Calculate 30% of your annual income
30% of $50,000 = 0.30 * $50,000 = $15,000

So, the maximum annual mortgage payment you can afford is $15,000.

Next, we need to determine the maximum loan amount you can borrow based on this annual payment and the interest rate.

Step 2: Calculate the monthly mortgage payment
To calculate the monthly mortgage payment, we'll use the formula for a fixed-rate mortgage:

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

Where:
M = monthly mortgage payment
P = loan amount
r = monthly interest rate
n = total number of months (in this case, 30 years = 360 months)

Let's break it down:

Step 3: Convert the annual interest rate to a monthly rate
Divide the annual interest rate by 12 (months).
5% / 100 = 0.05
0.05 / 12 = 0.0041667 (approximately)

So, the monthly interest rate is approximately 0.0041667.

Step 4: Calculate the loan amount
Using the calculated monthly interest rate and a 30-year (360 months) mortgage term, we can use an online mortgage calculator or a spreadsheet to find the loan amount that corresponds to a monthly payment of $15,000 (the maximum you can afford).

After plugging in the given values, the maximum loan amount would be determined.

Please note that this is a simplified explanation, and actual mortgage loan applications may involve additional factors such as credit score, down payment, debt-to-income ratio, and specific lender requirements. It is advisable to consult with a mortgage professional to get an accurate assessment of your borrowing capacity.