If the current interest rate is 5% for a 30-year mortgage loan, what is the maximum amount one can borrow for a house?

That depends upon the borrower's income and assets.

Current rate is 5% for a 30 year mortgage loan what is the maximum one can borrow with annual income of 50,000?

To determine the maximum amount one can borrow for a house, we need to consider a few factors, such as the interest rate, loan term, and the borrower's ability to make monthly payments.

First, let's calculate the monthly payment. We can use a mortgage calculator or a mathematical formula to do this. The formula for calculating the monthly payment is:

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

Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of monthly payments (loan term in years multiplied by 12)

In this case, the interest rate is given as 5% and the loan term is 30 years. Let's assume the borrower plans to make a down payment of 20%, which means they need a loan amount that covers 80% of the house price.

To find the maximum loan amount, we can start by calculating the monthly payment using these values. Let's assume the house price is $X. The loan amount would be 80% of $X, which is 0.8*X. Plugging in the values, the formula becomes:

M = 0.8*X [ (0.05/12)(1+(0.05/12))^(30*12) ] / [ (1+(0.05/12))^(30*12) - 1 ]

Now, we need to consider the borrower's ability to make monthly payments. Lenders typically use a debt-to-income (DTI) ratio to determine if a borrower can afford the monthly payments. The DTI ratio is the percentage of the borrower's monthly income that goes toward debt payments.

The maximum DTI ratio varies among lenders but is usually around 43%. Let's assume the borrower's monthly income is $Y. To calculate the maximum monthly payment they can afford, we multiply their income by the DTI ratio: 0.43 * $Y.

Now, we can set up an equation where the monthly payment (M) is equal to the maximum affordable monthly payment:

0.8*X [ (0.05/12)(1+(0.05/12))^(30*12) ] / [ (1+(0.05/12))^(30*12) - 1 ] = 0.43 * $Y

Solving this equation for X will give us the maximum amount that can be borrowed for a house given the interest rate, loan term, down payment, and the borrower's income. You can plug in the values and solve it using a calculator or a mathematical software to find the specific amount.