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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

In terms of paying less in interest, which is more economical for a $$ 150,000\( mortgage: a 30 -year fixed-rate at \)8 \%\( or a 20 -year fixed-rate at \)7.5 \%$ ? How much is saved in interest?

The price of a color printer is reduced by \(30 \%\) of its original price. When it still does not sell, its price is reduced by \(20 \%\) of the reduced price. The salesperson informs you that there has been a total reduction of \(50 \%\). Is the salesperson using percentages properly? If not, what is the actual percent reduction from the original price?

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?

To borrow money, you pawn your mountain bike. Based on the value of the bike, the pawnbroker loans you \(\$ 552\). One month later, you get the bike back by paying the pawnbroker \(\$ 851\). What annual interest rate did you pay?

The price of a small cabin is \(\$ 100,000\). The bank requires a \(5 \%\) down payment. The buyer is offered two mortgage options: 20 -year fixed at \(8 \%\) or 30 -year fixed at \(8 \%\). Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 20-year option?
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