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.

Question

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

Answer 1

To find the principal amount \( P \) that will generate $40 in simple interest, we can use the simple interest formula:

\[ I = Prt \]

We know:

• \( I = 40 \) (the interest),
• \( r = 0.10 \) (the interest rate in decimal form, which is 10%),
• \( t = 5 \) (the time in years).

We can rearrange the formula to solve for \( P \):

\[ P = \frac{I}{rt} \]

Now, substituting in the known values:

\[ P = \frac{40}{0.10 \times 5} \]

Calculating \( rt \):

\[ rt = 0.10 \times 5 = 0.5 \]

Now substituting this back into the equation for \( P \):

\[ P = \frac{40}{0.5} = 80 \]

Thus, the amount of money \( P \) that will generate $40 in interest at a 10% interest rate over 5 years is $80.