Question

Simple interest can be found with the formula A(t) = P(1 + rt). A is the amount in the account, P is the principal, r is the interest rate, and t is time. Ronald has $200 in a savings account that earns interest at 1% a year. Write a linear function to model the amount of money in his savings account at any time t.

a. Rewrite r as a decimal.

Answer 1

The simple interest formula is A(t) = P(1 + rt), where A is the amount, P the principal, r the interest rate, and t the time. For Ronald's $200 at 1% interest per year, the function becomes A(t) = 200(1 + 0.01t). After 5 years, the total amount would be $210.

Step-by-step explanation:

To create a linear function that models the amount of money in Ronald's savings account at any given time t, we need to use the simple interest formula which is A(t) = P(1 + rt). In Ronald's case, the principal P is $200 and the interest rate r is 1% per year. First, we must convert the annual interest rate into decimal form by dividing by 100, so 1% becomes 0.01.

Now, we can plug in the values into the formula to get the linear function for Ronald's savings account: A(t) = 200(1 + 0.01t). This equation allows us to calculate the total amount of money in the account, including principal and interest, after t years.

Example Application

Using the formula, if Ronald keeps his money in the account for 5 years, the interest earned would be calculated as follows:

• Interest = Principal × rate × time
• Interest = $200 × 0.01 × 5 = $10

The total amount in the account after 5 years would be:

• A(5) = 200(1 + 0.01 × 5)
• A(5) = 200(1 + 0.05)
• A(5) = 200 × 1.05
• A(5) = $210