Question

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

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**.