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Chapter 1: Problem 36

$$ 9000\( earning \)5 \%$ annual simple interest for 8 years.

Short Answer

Expert verified
The interest earned is 3600.

Step by step solution

01

- Identify the formula for simple interest

The formula for simple interest is given by: \[ I = P \times r \times t \] where, P = Principal amount r = Annual interest rate (in decimal form) t = Time (in years)
02

- Substitute the given values

Substitute the given values into the formula: P = 9000, r = 0.05 (since 5% = 0.05 in decimal), and t = 8.
03

- Calculate the interest

Calculate the interest: \[ I = 9000 \times 0.05 \times 8 \] \[ I = 3600 \] So, the interest earned is 3600.

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Key Concepts

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

Simple Interest Formula
To calculate simple interest, we use the following formula:

\[ I = P \times r \times t \]

Here, \(\text{I}\) represents the interest earned or paid.

The formula is quite straightforward. You multiply the principal amount \(\text{P}\) by the annual interest rate \(\text{r}\) and then by the time \(\text{t}\) in years.

This method is called 'simple' because it means that the interest is not compounded - the interest is calculated only on the principal amount each year.
Annual Interest Rate
The annual interest rate is a key factor in the simple interest formula. It's typically expressed as a percentage.

When using the simple interest formula, convert the annual interest rate into a decimal. For example, a 5% interest rate becomes 0.05.

This conversion is necessary because the formula is designed to work with decimals. If you leave the interest rate as a percentage, your calculations will be incorrect.

So, always remember:
  • Convert the percentage rate to a decimal rate before using it in the formula.
  • Divide the percentage by 100 to do this.
Principal Amount
The principal amount \( P \) is the initial sum of money that is either invested or borrowed, before any interest is applied.

In this exercise, the principal amount is $9000.

It is the base amount on which the interest will be calculated. This makes it a very important part of the simple interest formula.

Whatever amount you start with is your principal amount. More principal means more potential interest in the end.
Time in Years
The time \( t \) in the formula refers to the number of years for which the interest is calculated.

In simple interest calculations, time needs to be consistent. Always use years.

In this example, we calculate interest over 8 years.

Using years allows the formula to be straightforward. For other periods (like months or days), you would convert them into years. For instance:
  • For months, divide by 12.
  • For days, divide by 365.
This consistency helps maintain accuracy in your interest calculations.

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