The formula used to calculate simple interest is modeled by I=prt, where I=simple interest, p=principle, r=interest rate, and t=time, measured in years. Which of the following options represent(s) an alternative equivalent version of the simple interest formula? Select all that apply.

Question

p = i/rt
I - rt = p
I = trp
I = p + rt
t= i/rp

Answer 1

To find alternative equivalent versions of the simple interest formula \( I = prt \), we can manipulate the formula to solve for \( p \), \( r \), \( t \), or verify the equivalence of different phrases. Here are the derived equations along with their explanations:

1. \( p = \frac{I}{rt} \)

   • Rearranging the original equation \( I = prt \) gives \( p = \frac{I}{rt} \), which is correct.

2. \( I - rt = p \)

   • This is incorrect. The equation rearranging from \( I = prt \) would not yield \( I - rt = p \).

3. \( I = trp \)

   • This rearrangement is incorrect. While the equation is algebraically consistent with multiplication, it doesn’t represent the original context accurately.

4. \( I = p + rt \)

   • This is incorrect. The original equation \( I = prt \) does not relate \( I \) as the sum of \( p \) and \( rt \).

5. \( t = \frac{I}{pr} \)

   • Rearranging \( I = prt \) gives \( t = \frac{I}{pr} \), which is correct.

Therefore, the correct options representing an equivalent version of the simple interest formula are:

• \( p = \frac{I}{rt} \)
• \( t = \frac{I}{pr} \)