Simple Interest and Inequalities

The video tutorial explains how to calculate simple interest using the formula A = P + PRT, where A is the account balance after T years, P is the principal, R is the annual interest rate, and T is the time in years. Emanuel wants to invest in a savings account with a 3% interest rate for 10 years to achieve a balance of at least $20,000. The tutorial sets up and solves an inequality to determine the minimum principal Emanuel needs to deposit, rounding the result to whole dollars. The solution shows that Emanuel must deposit at least $15,385 to meet his goal.

What does the variable 'a' represent in the simple interest formula?

• The annual interest rate

• The initial amount invested

• The time in years

• The balance after a certain period

In Emanuel's scenario, what is the annual interest rate expressed as a decimal?

• 0.03

• 0.003

• 0.3

• 3

What is the time period for which Emanuel plans to leave his investment?

• 5 years

• 10 years

• 15 years

• 20 years

Which of the following represents the inequality set up to find the principal amount?

• p + 0.3p ≥ 20000

• p + 0.3p = 20000

• p + 0.3p < 20000

• p + 0.3p > 20000

How do you simplify the expression p + 0.3p?

• 0.3p

• 1.3p

• p

• 3p

What operation is performed to isolate 'p' in the inequality 1.3p ≥ 20000?

• Subtract 1.3 from both sides

• Multiply both sides by 1.3

• Divide both sides by 1.3

• Add 1.3 to both sides

What is the result of dividing 20000 by 1.3?

• 15200

• 15385

• 15000

• 15400

Why is it necessary to round up the calculated principal amount?

• To ensure the balance is exactly 20000

• To avoid a balance less than 20000

• To make calculations easier

• To match the interest rate

What is the minimum amount Emanuel needs to deposit to achieve his savings goal?

• 15000

• 15385

• 20000

• 18000

What would happen if Emanuel rounded down the principal amount?

• He would have more than 20000 after 10 years

• He would have exactly 20000 after 10 years

• He would have less than 20000 after 10 years

• The interest rate would increase