To compare the simple interest and compound interest, we can use the formulas for each.
Simple Interest Formula:
\[ \text{SI} = P \times r \times t \] Where:
- \( P \) = principal amount ($4,300)
- \( r \) = annual interest rate (7.5% = 0.075)
- \( t \) = time in years (2 years)
Calculating simple interest: \[ \text{SI} = 4300 \times 0.075 \times 2 \] \[ \text{SI} = 4300 \times 0.15 \] \[ \text{SI} = 645 \]
Now, calculate the total balance after 2 years: \[ \text{Total Balance (SI)} = P + \text{SI} = 4300 + 645 = 4945 \]
Compound Interest Formula:
\[ \text{CI} = P \times (1 + r)^t \] Where:
- \( P \) = principal amount ($4,300)
- \( r \) = annual interest rate (7% = 0.07)
- \( t \) = time in years (2 years)
Calculating compound interest: \[ \text{CI} = 4300 \times (1 + 0.07)^2 \] \[ \text{CI} = 4300 \times (1.07)^2 \] \[ \text{CI} = 4300 \times 1.1449 \] (approximately) \[ \text{CI} \approx 4923.07 \]
Summary of Results:
- The total balance with simple interest at 7.5% after 2 years is $4,945.
- The total balance with compound interest at 7% after 2 years is approximately $4,923.07.
Conclusion: Simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment.
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