Problem 10 - Prealgebra

Question

A These problems are similar to the examples found in this section. They should be set up and solved in the same way. (Problems 1-12 involve simple interest.) Short-Term Loan If a loan of \(\$ 1,200\) at \(9 \%\) is paid off in 90 days, what is the interest?

Step-by-Step Solution

Answer

The interest on the loan is \(\$26.64\).

Step 1: Identifying Variables

We need to find the interest on a short-term loan of \(\\(1200\) at an interest rate of \(9\%\) for 90 days. The formula for simple interest is \(I = P \times r \times t\), where \(I\) is the interest, \(P\) is the principal amount (\\)1200), \(r\) is the annual interest rate as a decimal (\(0.09\)), and \(t\) is the time in years.

Step 2: Converting Days to Years

The time \(t\) should be in years for the formula, and there are 365 days in a year. Convert 90 days into years by dividing 90 by 365: \(t = \frac{90}{365}\).

Step 3: Applying the Simple Interest Formula

Substitute \(P = 1200\), \(r = 0.09\), and \(t = \frac{90}{365}\) into the formula \(I = P \times r \times t\):\[I = 1200 \times 0.09 \times \frac{90}{365}\].

Step 4: Calculating the Interest

Calculate the expression:First, find \(\frac{90}{365} = 0.2466\). Next, multiply the results: \(I = 1200 \times 0.09 \times 0.2466\) which equals \(\$26.64\).

Key Concepts

loan interest calculation

Loan interest calculation might sound like a huge task, but it's quite simple if you follow some basic steps. When you borrow money, the lender charges an amount for providing the funds, which is known as interest. The calculation helps in understanding how much extra money you'll need to repay in addition to the borrowed amount.

The core of loan interest calculation is the Simple Interest Formula. Simple interest is easy to calculate and is often used for short-term loans. The formula is given as:

• \( I = P \times r \times t \)

Where:

• \( I \) is the interest amount to be paid.
• \( P \) is the principal amount (the initial loan amount).
• \( r \) is the annual interest rate (expressed as a decimal), so 9% becomes 0.09.
• \( t \) is the time period the interest is calculated for, in years.

This formula helps in figuring out the simple interest quickly, avoiding complicated procedures and getting straight to the result.

short-term loan

A short-term loan is a type of loan intended to be repaid within a short period, typically within a year. This makes them a good choice for immediate but temporary financial needs. Unlike long-term loans that might be accompanied by more stringent terms and conditions, short-term loans provide a quicker financial boost.

Such loans are convenient for several reasons:

• Faster approval and processing: Often, short-term loans are approved faster compared to long-term financial products.
• Simple structure: With fewer complications in their structure, they make it simpler to understand the repayments and interest calculations.
• Less interest paid overall: While they might have a higher interest rate, the total interest paid is often lower because the loan period is shorter.

However, the catch is to ensure timely repayments to avoid the consequences of higher penalty rates or fees.

interest formula calculation

Understanding the interest formula calculation is crucial when dealing with any kind of loan, especially for students tackling related problems in mathematics or finance. The given problem, with a loan of \(\\(1200\) at 9% interest rate for 90 days, demonstrates the importance of correctly applying the steps in calculation.

Here’s a breakdown of the example calculation:

• Start by identifying the values for the formula: Principal \( P = 1200 \), Rate \( r = 0.09 \) (since 9% must be converted to a decimal).
• Estimate the time period in years: Since the interest period given is 90 days, and a year has 365 days, convert it to years: \( t = \frac{90}{365} \).
• Substitute these into the interest formula: \[ I = 1200 \times 0.09 \times \frac{90}{365} \]
• Calculate step-by-step: First, compute the time in years which is approximately 0.2466 years. Then multiply 1200 by 0.09 and the result by 0.2466.

This offers an interest of \(\\)26.64\), clearly showing how each step contributes to finding the answer. Familiarity with this calculation ensures precision and boosts confidence in managing finances effectively.