Question**: A bank account earns simple interest at a rate of 5% per annum. If $1,200 is deposited, how much interest is earned in 3 years? - Coaching Toolbox

Understanding the Context

Simple interest is calculated only on the original principal amount throughout the investment period. Unlike compound interest, which earns interest on both the principal and accumulated interest, simple interest keeps the Math clean and predictable.

The formula for simple interest is:
\[
\ ext{Interest} = P \ imes r \ imes t
\]
Where:
- \( P \) = Principal amount (initial deposit)
- \( r \) = Annual interest rate (as a decimal)
- \( t \) = Time in years

Applying the Formula to Your Scenario

Let’s break down the details for a $1,200 deposit earning 5% interest per year over 3 years:

Key Insights

• Principal (P): \$1,200
  - Annual interest rate (r): 5% = 0.05
  - Time (t): 3 years

Using the simple interest formula:
\[
\ ext{Interest} = 1200 \ imes 0.05 \ imes 3
\]

First, multiply the rate and time:
\[
0.05 \ imes 3 = 0.15
\]
Then multiply by the principal:
\[
1200 \ imes 0.15 = 180
\]

Result: Interest Earned in 3 Years
The bank earns \$180 in simple interest over 3 years on a \$1,200 deposit at 5% per annum.

Final Thoughts

Why Knowing This Matters

Understanding how interest accrues helps in:
- Making informed savings decisions
- Calculating loan repayments
- Planning for short-term financial goals

Remember, simple interest is ideal for short-term investments and personal savings accounts where consistent, predictable returns matter most.

If you’re exploring interest-earning opportunities, use this formula to estimate returns quickly—your financial planning will benefit from clarity and confidence!

Key Takeaway:
For a \$1,200 deposit at 5% simple interest, \$180 is earned in 3 years. Time your savings wisely!