Question

Write an expression to represent the amount owed by a homeowner who borrows $2,000 with 4% interest, without making payments, after x years. Use the formula y = a * b^x, where y is the total amount, a is the starting amount, b is the growth factor (1 + percent), and x is time in years.

Answer 1

The expression representing the total amount owed by a homeowner who borrows $2,000 at 4% interest after x years is y = 2000 * 1.04^x.

Step-by-step explanation:

To write an expression representing the total amount owed by a homeowner who borrows $2,000 at 4% interest without making payments after x years, we can apply the formula y = a * b^x. Here, y is the total amount, a is the initial amount borrowed, b is the growth factor which is 1 + the interest rate as a decimal, and x is the number of years.

For the given situation, the homeowner borrows $2,000 and the interest rate is 4%, or 0.04 in decimal form. Therefore, the growth factor b is 1.04. The formula becomes y = 2000 * 1.04^x. This is the expression that represents the total amount owed after x years with the interest compounded annually.