Using a 5% interest rate, a 30-year term, and a monthly payment of 313, what is the maximum loan amount described?

Using a 5% interest rate, a 30-year term, and a monthly payment of 313, what is the maximum loan amount described?

• A. $58,306
• B. $62,653
• C. $50,000
• D. $60,000

Answer: (D)

The amount you can borrow is the present value of the fixed monthly payments given the interest rate and term. Use the fixed-rate mortgage payment formula and solve for the loan amount. P = L * r / (1 - (1 + r)^-n) Where: - P is the monthly payment - L is the loan amount - r is the monthly interest rate (annual rate divided by 12) - n is the total number of payments (years × 12) Solve for L: L = P * (1 - (1 + r)^-n) / r Plugging in the numbers: - r = 0.05 / 12 = 0.0041667 - n = 30 × 12 = 360 - (1 + r)^-n ≈ (1.0041667)^-360 ≈ 0.2238 - 1 - (1 + r)^-n ≈ 0.7762 L ≈ 313 × 0.7762 / 0.0041667 ≈ 58,300 So the maximum loan amount is about $58,300, which is closest to $58,306.

The amount you can borrow is the present value of the fixed monthly payments given the interest rate and term. Use the fixed-rate mortgage payment formula and solve for the loan amount.

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

Where:

• P is the monthly payment

• L is the loan amount

• r is the monthly interest rate (annual rate divided by 12)

• n is the total number of payments (years × 12)

Solve for L:

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

Plugging in the numbers:

• r = 0.05 / 12 = 0.0041667

• n = 30 × 12 = 360

• (1 + r)^-n ≈ (1.0041667)^-360 ≈ 0.2238

• 1 - (1 + r)^-n ≈ 0.7762

L ≈ 313 × 0.7762 / 0.0041667 ≈ 58,300

So the maximum loan amount is about $58,300, which is closest to $58,306.