Question

The monthly payments, p dollars, on a mortgage in which A dollars were borrowed at an annual interest rate of r% for t years is given by P = f(A, r, t). Is fan increasing or decreasing function of A?

Answer 1

The monthly payments on a mortgage, represented by the function P = f(A, r, t), are an increasing function of the borrowed amount A.

Step-by-step explanation:

The function P = f(A, r, t) represents the monthly payments on a mortgage. To determine whether the function is increasing or decreasing with respect to A, we need to consider the partial derivative of P with respect to A.

The partial derivative ∂P/∂A represents the rate of change of P with respect to A. If ∂P/∂A is positive, the function is increasing with respect to A. If ∂P/∂A is negative, the function is decreasing with respect to A.

To find the partial derivative, we differentiate the function P = f(A, r, t) with respect to A:

∂P/∂A = r * (1+r)^t / ((1+r)^t - 1)

By examining the partial derivative, we can see that it is always positive, which means the function P = f(A, r, t) is an increasing function of A. This implies that as the borrowed amount A increases, the monthly payments P will also increase.