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Chapter 8: Problem 2

In Exercises \(1-8\), the principal \(P\) is borrowed at simple interest rater for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year. \(P=\$ 7000, r=5 \%, t=1\) year

Short Answer

Expert verified
The simple interest owed for the use of the money is $350

Step by step solution

01

Understand the given variables

Firstly, identify the given variables. Here, the principal \(P\) is $7000, the rate of interest \(r\) is 5%, and the time period \(t\) is 1 year.
02

Convert Percentage to Decimal

The rate \(r\) of interest needs to be used in decimal form, so we convert 5% to decimal. This is done by dividing the percentage by 100, so \(r = 5/100 = 0.05\)
03

Substitute All Values into the Interest Formula

Now we substitute the values of \(P\), \(r\), and \(t\) into the formula \(I=Prt\). This gives us \(I=7000*0.05*1\)
04

Calculate the Interest

Upon calculation, we find that \(I=350\), so the interest owed for the use of the money is $350.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Interest Rate
The interest rate is a crucial component in calculating simple interest. It represents the percentage charged on the principal amount for borrowing money over a specific period. In simple interest, the interest rate is always constant throughout the entire period, unlike compound interest where it can vary over time.
To use the interest rate in calculations, it's essential to convert it from a percentage to a decimal.
  • Divide by 100 - For instance, an interest rate of 5% becomes 0.05 in decimal form.
This conversion is fundamental because it allows us to perform accurate calculations mathematically. Ensuring you're using the decimal form in formulas avoids mistakes in computing the interest.
Principal Amount
The principal amount is the initial sum of money loaned or deposited. This is the base number that the interest will be calculated on. In simple interest scenarios, the principal remains unchanged throughout the borrowing period. For example, if you borrow $7000, this is your principal amount, and it will not fluctuate.
Understanding the principal is key because it underscores the foundation of interest calculations. The larger the principal, the higher the amount of interest accrued, assuming the interest rate and time period remain constant. Thus, borrowers need to be mindful of the principal amount as it significantly determines the overall cost of borrowing.
Time Period
The time period in simple interest calculations refers to the length of time for which the money is borrowed or invested. It鈥檚 typically expressed in years, making it straightforward to integrate into the simple interest formula.
To ensure correctness in interest calculation, ascertain the time period is consistent with how the interest rate is defined. If the interest rate is annual, then the time should be in years. Converting time into the correct unit prevents errors. For example, borrowing for 1 year is directly used in the formula as t = 1.
In calculations based on a standard 360-day year, make sure to align your figures accordingly if any conversions are necessary.
Interest Calculation
Calculating simple interest involves a straightforward formula that requires the interest rate, principal amount, and time period. The formula for simple interest is:\[ I = P \cdot r \cdot t \]where:
  • I is the interest
  • P is the principal amount
  • r is the interest rate (as a decimal)
  • t is the time period
The beauty of simple interest is in this simplicity: multiply these three factors to find the interest owed. For example, with a principal of \(7000, an interest rate of 5%, and a time period of 1 year, substitute these into the formula to get: \[ I = 7000 \times 0.05 \times 1 = 350 \]This means the interest owed will be \)350. This linear calculation method keeps it easy to understand and apply in various situations.

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Most popular questions from this chapter

Suppose that at age 25 , you decide to save for retirement by depositing \(\$ 50\) at the end of each month in an IRA that pays \(5.5 \%\) compounded monthly. a. How much will you have from the IRA when you retire at age \(65 ?\) b. Find the interest.

You would like to have \(\$ 4000\) in four years for a special vacation following college graduation by making deposits at the end of every six months in an annuity that pays \(7 \%\) compounded semiannually. a. How much should you deposit at the end of every six months? b. How much of the \(\$ 4000\) comes from deposits and how much comes from interest?

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What are the two components of liability coverage and what is covered by each component?

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