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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

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?

When you buy something, it actually costs more than you may think - at least in terms of how much money you must earn to buy it. For example, if you pay \(28 \%\) of your income in taxes, how much money would you have to earn to buy a used car for \(\$ 7200\) ?

In Exercises 3-4, find the gross income, the adjusted gross income, and the taxable income. Base the taxable income on the greater of a standard deduction or an itemized deduction. Suppose your neighbor earned wages of \(\$ 319,150\), received \(\$ 1790\) in interest from a savings account, and contributed \(\$ 4100\) to a tax-deferred retirement plan. He is entitled to a personal exemption of \(\$ 3800\) and the same exemption for each of his two children. He is also entitled to a standard deduction of \(\$ 5950\). The interest on his home mortgage was \(\$ 51,235\), he contributed \(\$ 74,000\) to charity, and he paid \(\$ 12,760\) in state taxes.

Exercises 19 and 20 refer to the stock tables for Goodyear (the tire d. How many shares of this company's stock were traded company) and Dow Chemical given below. In each exercise, use yesterday? the stock table to answer the following questions. Where necessary, e. What were the high and low prices for a share yesterday? round dollar amounts to the nearest cent. f. What was the price at which a share last traded when the stock a. What were the high and low prices for a share for the past exchange closed yesterday? b. If you owned 700 shares of this stock last year, what dividend g. What was the change in price for a share of stock from the did you receive? h. Compute the company's annual earnings per share using c. What is the annual return for the dividends alone? How does Annual earnings per share this compare to a bank offering a \(3 \%\) interest rate? $$ =\frac{\text { Yesterday's closing price per share }}{P E \text { ratio }} . $$ $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \text { 52-Week High } & \text { 52-Week Low } & \text { Stock } & \text { SYM } & \text { Div } & \text { Yld \% } & \text { PE } & \text { Vol 100s } & \text { Hi } & \text { Lo } & \text { Close } & \text { Net Chg } \\ \hline 73.25 & 45.44 & \text { Goodyear } & \text { GT } & 1.20 & 2.2 & 17 & 5915 & 56.38 & 54.38 & 55.50 & +1.25 \\ \hline \end{array} $$

If a three-year car loan has the same interest rate as a six-year car loan, how do the monthly payments and the total interest compare for the two loans?
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