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Chapter 8: Problem 23

\(A=\$ 14,000, r=9.5 \%, t=6\) years

Short Answer

Expert verified
The simple interest earned on the principal amount of \$14,000 with an annual interest rate of 9.5% over 6 years is \$7980.

Step by step solution

01

Understand the formula

The simple interest formula is \(I = P*r*t\). This formula allows us to calculate the interest earned on a principal amount (P) over a fixed period (t) at a certain interest rate (r). The rate is usually annual, but it can also be monthly, daily, etc. In the given problem, the rate is annual.
02

Substitute the given values

Next, the given values can be substituted into the formula: \(P=\$14,000\), \(r=9.5% = 0.095\), and \(t=6\) years. Therefore, the formula becomes \(I=\$14,000*0.095*6\).
03

Calculate the interest

Once the values are substituted, the Interest (I) can be found out by multiplying the given inputs: \(I=\$14,000*0.095*6 = \$7980\).

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Key Concepts

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

Interest Calculation
Simple interest is a way to calculate the interest earned or paid on a principal amount. This interest comes from a fixed percentage, called the interest rate, applied over a certain time period. The formula used for calculating simple interest is: \(I = P \times r \times t\). Here, \(I\) represents the interest amount, \(P\) stands for the principal amount, \(r\) is the interest rate, and \(t\) is the time the money is invested or borrowed for. When using this formula, make sure to convert percentages into decimal form to calculate easily.
  • For example, 9.5% converts to 0.095 when used in calculations.
  • Multiply the principal by the rate, then by the time period to find the interest.
This straightforward approach makes it a common choice for basic interest calculations.
Principal Amount
The principal amount is the initial sum of money invested or loaned. It is the base on which interest is calculated. In the context of simple interest, understanding the principal is crucial because it forms the foundation for all further calculations. In the given example, the principal is \(\$14,000\).
  • This is the starting amount before any interest is added.
  • The same amount is used for multiplying with the interest rate and time period to find the total interest.
Knowing the principal lets you estimate how much interest you'll earn or owe during the term.
Annual Interest Rate
The annual interest rate is the percentage of the principal charged as interest each year. It is typically expressed as a percentage and dictates how much extra money the principal earns each year. For precise calculations, the rate must be converted from a percentage to a decimal. In the solution provided:
  • The given interest rate is 9.5%, which is converted to 0.095 for calculations.
  • This rate applies annually, meaning each year, 9.5% of the principal is added as interest.
Being aware of the interest rate and its conversion is essential for accurately determining how interest accumulates over time.
Time Period in Years
The time period in years reflects how long the principal is invested or borrowed. In simple interest, this time period directly affects how much total interest will be generated. Since simple interest is usually calculated on a yearly basis, it's important to specify the length of time clearly in years. For the exercise problem:
  • The time period given is 6 years.
  • This span means that interest at the given rate is added every year for 6 years.
Understanding how long the money remains invested or borrowed can significantly alter the total interest calculation, making this aspect vital in financial planning.

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Most popular questions from this chapter

a. Suppose that between the ages of 22 and 40 , you contribute \(\$ 3000\) per year to a \(401(\mathrm{k})\) and your employer contributes \(\$ 1500\) per year on your behalf. The interest rate is \(8.3 \%\) compounded annually. What is the value of the \(401(\mathrm{k})\), rounded to the nearest dollar, after 18 years? b. Suppose that after 18 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the \(401(\mathrm{k})\). How much money, to the nearest dollar, will you have in the plan when you reach age 65 ? c. What is the difference between the amount of money you will have accumulated in the \(401(\mathrm{k})\) and the amount you contributed to the plan?

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Make Sense? In Exercises 23-26, determine whether each statement makes sense or does not make sense, and explain your reasoning. There must be an error in the loan amortization schedule for my mortgage because the annual interest rate is only \(3.5 \%\), yet the schedule shows that I'm paying more on interest than on the principal for many of my payments.

Describe two aspects of responsible credit card use.

How much should you deposit at the end of each month in an IRA that pays \(8 \%\) compounded monthly to earn \(\$ 60,000\) per year from interest alone, while leaving the principal untouched, when you retire in 30 years?
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