Question

the balance of a car loan, B(x), as it relates to time in years, x, is described by the equation B(x)= A(1-r)ʷhere A is the original amount of the loan and r is the interest rate written as a decimal. Solve this equation for A.

Answer 1

To solve for A in the equation B(x) = A(1-r)^x, divide both sides by (1-r)^x, giving A = B(x)/(1-r)^x.

Step-by-step explanation:

To solve the equation B(x) = A(1-r)^{x} for A, the original amount of the loan, we need to isolate A on one side of the equation.

To do this, you divide both sides of the equation by (1-r)^{x}. This gives you A = \frac{B(x)}{(1-r)^{x}}. Therefore, to find the original loan amount, A, you take the current balance of the car loan, B(x), and divide it by (1-r)^{x}, where r is the interest rate as a decimal, and x is the time in years since the loan was taken out.

To solve the equation B(x) = A(1-r)^w for A, we need to isolate A on one side of the equation. Here are the steps:

Divide both sides of the equation by (1-r) to get B(x) / (1-r) = A.

Therefore, A = B(x) / (1-r).

So, to find the original amount of the loan (A), you divide the balance of the car loan (B(x)) by (1-r), where r is the interest rate written as a decimal. This formula allows you to calculate the original loan amount when you know the balance and interest rate.