Problem Statement:
We need to determine how much money was invested at a 6% annual simple interest rate for 3 years to earn $3870 in interest.
Known Information:
- Interest earned (\( I \)) = $3870
- Annual interest rate (\( r \)) = 6% = 0.06 (in decimal form)
- Time period (\( t \)) = 3 years
Formula for Simple Interest:
The formula for calculating simple interest is:
\[
I = P \cdot r \cdot t
\]
where:
- \( I \) is the interest earned,
- \( P \) is the principal amount (the initial investment),
- \( r \) is the annual interest rate (in decimal form),
- \( t \) is the time period in years.
Goal:
We need to solve for the principal amount \( P \).
Step-by-Step Solution:
1.
Substitute the known values into the formula:
\[
I = P \cdot r \cdot t
\]
\[
3870 = P \cdot 0.06 \cdot 3
\]
2.
Simplify the right-hand side:
\[
3870 = P \cdot 0.18
\]
3.
Solve for \( P \):
To isolate \( P \), divide both sides of the equation by 0.18:
\[
P = \frac{3870}{0.18}
\]
4.
Perform the division:
\[
P = \frac{3870}{0.18} = 21500
\]
Final Answer:
The amount of money invested is:
\[
\boxed{21500}
\]
Explanation:
- The formula \( I = P \cdot r \cdot t \) relates the interest earned to the principal, rate, and time.
- By substituting the given values and solving for \( P \), we find that an investment of $21,500 at 6% annual simple interest for 3 years will yield $3870 in interest.
This solution ensures that all steps are clear and mathematically sound.
Parent Tip: Review the logic above to help your child master the concept of simple interest math problems worksheet.
