Solve Simple Interest Problems

How to Solve Simple Interest Problems: A Step-by-Step Guide

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Interest is money paid regularly at a particular rate for borrowing money or delaying the repayment of a debt. In this article, we will explore how to calculate simple interest.

Step 1: Understanding the Formula

The simple interest ($I$) is calculated by using the following formula:

$$I = P \cdot r \cdot t$$

Where:

• $P$ is the principal amount (the initial amount of money)
• $r$ is the annual interest rate (in decimal form)
• $t$ is the time the money is invested or borrowed for, in years.

Step 2: Plug in the Values

Substitute the given values into the formula. Make sure the interest rate is converted into decimal form by dividing it by 100, and the time is in years.

Step 3: Do the Calculation

Multiply the principal amount ($P$) by the interest rate ($r$) and then by the time period ($t$). The result will be the simple interest ($I$).

Step 4: Interpret the Result

The result you get is the amount of simple interest. If the question asks for the total amount accumulated, you would add the simple interest to the principal amount.

$$A = P + I$$

where $A$ is the total amount.

Let's say you want to calculate the simple interest for a principal amount of $$1000$ invested at an annual interest rate of $5%$ for $3$ years.

1. Identify the principal amount, interest rate, and time. Here, $P = \$1000$, $r = 5\% = 0.05$, and $t = 3$ years.
2. Substitute the values into the formula.

$$I = P \cdot r \cdot t = \$1000 \cdot 0.05 \cdot 3 = \$150$$

So, the simple interest earned in $3$ years is $$150$.

If you want to find the total amount after 3 years, you can add this interest to the initial principal amount:

$$A = P + I = \$1000 + \$150 = \$1150$$

So, the total amount after $3$ years would be $$1150$.

Exercises

1) How much interest would you earn on $\$2000$ invested at an annual interest rate of $3\%$ for 4 years?

1) If you invest $\$5000$ at an annual interest rate of $4\%$ for 5 years, what would be the interest?

1) Find the interest earned from $\$3000$ invested at an annual interest rate of $5\%$ for 2 years.

1) How much interest would you receive if you invest $\$1500$ at an annual interest rate of $6\%$ for 3 years?

1) What is the interest earned on $\$1000$ invested at an annual interest rate of $2\%$ for 10 years?

1) If $\$8000$ is invested at an annual interest rate of $7\%$ for 1 year, what is the simple interest?

1) Find the simple interest for $\$6000$ invested at an annual interest rate of $3.5\%$ for 5 years.

1) What is the simple interest earned from $\$7500$ invested at an annual interest rate of $4.5\%$ for 3 years?

1) Calculate the interest for $\$9000$ invested at an annual interest rate of $5.5\%$ for 2 years.

1) If $\$12000$ is invested at an annual interest rate of $6.5\%$ for 4 years, what is the interest?