Questions: The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r, where r is expressed as a decimal. What is the amount of money, P, that will generate 40 in interest at a 10% interest rate over 5 years? 60 80 90 100

The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r, where r is expressed as a decimal. What is the amount of money, P, that will generate 40 in interest at a 10% interest rate over 5 years? 60 80 90 100
Transcript text: The simple interest formula is $I=$ Prt, where $I$ represents simple interest on an amount, $P$, for $t$ years at a rate of $r$, where $r$ is expressed as a decimal. What is the amount of money, $P$, that will generate $\$ 40$ in interest at a $10 \%$ interest rate over 5 years? $\$ 60$ $\$ 80$ $\$ 90$ \$100
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Solution

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Solution Steps

Step 1: Identify the given values

The given values are:

  • Simple interest \( I = \$40 \)
  • Interest rate \( r = 10\% = 0.10 \) (as a decimal)
  • Time \( t = 5 \) years
Step 2: Use the simple interest formula

The simple interest formula is: \[ I = Prt \] We need to solve for \( P \), the principal amount.

Step 3: Rearrange the formula to solve for \( P \)

Rearrange the formula to isolate \( P \): \[ P = \frac{I}{rt} \]

Step 4: Substitute the given values into the formula

Substitute \( I = 40 \), \( r = 0.10 \), and \( t = 5 \) into the formula: \[ P = \frac{40}{0.10 \times 5} \]

Step 5: Perform the calculation

Calculate the denominator: \[ 0.10 \times 5 = 0.50 \] Now, divide to find \( P \): \[ P = \frac{40}{0.50} = 80 \]

The principal amount \( P \) is \(\$80\).

Final Answer

\(\boxed{80}\)

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