Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Equations

College Algebra

1. Equations & Inequalities

Linear Equations

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1:55 minutes

Problem 59

Textbook Question

Work each problem. Elmer borrowed $3150 from his brother Julio to pay for books and tuition. He agreed to repay Julio in 6 months with simple annual interest at 4%.(a)How much will the interest amount to?

Verified step by step guidance

Step 1: Identify the formula for simple interest, which is I = P \times r \times t, where I is the interest, P is the principal amount, r is the rate of interest, and t is the time in years.

Step 2: Determine the principal amount (P). In this case, P = 3150 dollars.

Step 3: Determine the rate of interest (r). The problem states that the interest rate is 4%, which can be expressed as a decimal: r = 0.04.

Step 4: Determine the time period (t). Since the repayment is in 6 months, convert this time into years: t = \frac{6}{12} = 0.5 years.

Step 5: Substitute the values into the simple interest formula: I = 3150 \times 0.04 \times 0.5.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Simple Interest Formula

The simple interest formula is used to calculate the interest earned or paid on a principal amount over a specific period. It is expressed as I = PRT, where I is the interest, P is the principal amount, R is the annual interest rate (as a decimal), and T is the time in years. This formula is essential for determining how much interest Elmer will owe Julio after 6 months.

Principal Amount

The principal amount is the initial sum of money borrowed or invested, before any interest is applied. In this scenario, Elmer borrowed $3150, which serves as the principal for calculating the interest. Understanding the principal is crucial as it directly influences the total interest accrued over the loan period.

Time Period in Interest Calculations

In interest calculations, the time period is the duration for which the money is borrowed or invested, typically expressed in years. Since Elmer's loan is for 6 months, it is important to convert this time into years for the simple interest formula, which means using T = 0.5 years. This conversion is necessary to accurately compute the interest amount.