Find the amount (in $) of interest on the loan.
| Principal | Rate (%) | Time | Interest |
| :-------- | :------- | :------- | :------- |
| $90,000 | 7 \frac{3}{4} | 6 months | $ \square |
Answer (2)
Convert the annual interest rate to a decimal: 7.75% = 0.0775 .
Convert the loan duration to years: 6 months = 0.5 years.
Apply the simple interest formula: I n t eres t = P r in c i p a l × R a t e × T im e .
Calculate the interest amount: I n t eres t = 90000 × 0.0775 × 0.5 = 3487.5 .
Explanation
Understanding the Problem We are given a loan with a principal amount of $90,000, an annual interest rate of 7 4 3 % , and a loan duration of 6 months. Our goal is to find the amount of interest on the loan.
Converting Interest Rate to Decimal First, we need to convert the annual interest rate to a decimal. We have 7 4 3 % = 7.75% . To convert this percentage to a decimal, we divide by 100: r = 100 7.75 = 0.0775
Converting Time to Years Next, we need to express the loan duration in years. Since the loan duration is 6 months, which is half a year, we have: t = 12 6 = 0.5 years
Applying the Simple Interest Formula Now, we can calculate the simple interest using the formula: I n t eres t = P r in c i p a l × R a t e × T im e Substituting the given values into the formula, we get: I n t eres t = 90000 × 0.0775 × 0.5
Calculating the Interest Amount Calculating the interest amount: I n t eres t = 90000 × 0.0775 × 0.5 = 3487.5 Therefore, the amount of interest on the loan is $3487.50.
Examples
Understanding simple interest is crucial in many real-life scenarios. For instance, when you deposit money into a savings account, the bank pays you interest. Similarly, when you take out a loan, you are charged interest. Knowing how to calculate simple interest helps you understand the cost of borrowing money or the return on your investments. For example, if you deposit $1,000 into a savings account with an annual interest rate of 5% for 2 years, the simple interest earned would be $1,000 \times 0.05 \times 2 = $100. This knowledge empowers you to make informed financial decisions.
The total interest on the loan of $90,000 at an annual interest rate of 7.75% for 6 months is calculated to be $3,487.50 using the simple interest formula. This is done by converting the interest rate to a decimal and the loan duration to years, then applying the formula for interest. The significant steps include calculating the decimal form of the interest rate and converting months to years to solve.
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