Question

Suppose I deposit $500 into my bank account that earns 3% interest per year. Is the total amount in my bank account per year a linear relationship? Hint: use a table of values and look at the rate of change. Also, keep in mind that once you earn interest, the next year you will earn interest not only on your original investment but on the new amount.

Answer 1

The total amount in your bank account per year is not a linear relationship, it's compound interest.

Explanation:

The total amount in your bank account per year is not a linear relationship because it is not a straight line. Linear relationships are defined by an equation in the form of y = mx + b, where m is the slope of the line, x is the independent variable and y is the dependent variable, and b is the y-intercept.

In this case, the total amount in your bank account per year is not a straight line, it is a curve. The total amount in your bank account will increase as a function of time, but the rate of increase is not constant as it is with linear relationships.

The amount of money in your account will increase over time as the interest is compounded. The interest is calculated on the principal + accumulated interest, so the growth rate of the account is not constant, it increases as the balance grows.

For example, the first year you will earn $5000.03 = $15 in interest, and the second year you will earn $5150.03 = $15.45 in interest, the next year the interest will be $530.45*0.03 = $15.91 and so on.