Example Card: Finding the Total with Simple Interest
Calculate simple interest totals in Grade 9 algebra using A=P(1+rt). Find the total amount owed or earned after interest by multiplying principal by the combined rate-time factor.
Key Concepts
Simple interest is straightforward, but let's walk through finding the total amount, which is a common final step. This example will use the key idea of the simple interest formula.
Example Problem $15,000 is invested for 12 years at $3\%$ simple interest. How much money will be in the account after 12 years?
Step by Step 1. First, we need to find the interest earned. We'll use the simple interest formula, $I = Prt$. 2. The principal $P$ is $15,000$. The rate $r$ is $3\%$, which we write as the decimal $0.03$. The time $t$ is $12$ years. 3. Substitute these values into the formula: $$ I = 15000(0.03)(12) $$ 4. Simplify the expression to find the interest: $$ I = 5400 $$ 5. The account will earn $5,400$ dollars in interest. The question asks for the total amount in the account, so we add this interest to the original principal. $$ 15000 + 5400 = 20400 $$ 6. There will be $20,400$ dollars in the account after 12 years.
Common Questions
What is the simple interest formula and what do the variables mean?
Simple interest: I = Prt where P is principal, r is annual rate as a decimal, t is time in years. Total amount: A = P + I = P(1 + rt).
How do you find the total amount with simple interest?
Multiply the principal by (1 + rate × time). For $500 at 4% for 3 years: A = 500(1 + 0.04 × 3) = 500(1.12) = $560.
What is the difference between simple and compound interest?
Simple interest is calculated only on the principal. Compound interest earns interest on both principal and accumulated interest, growing faster. Simple interest produces linear growth.