To determine which method of interest (simple or compound) results in a higher balance after 2 years for an investment of $4,300, we will calculate both the simple interest and the compound interest.
Simple Interest Calculation
The formula for simple interest is:
\[ A = P(1 + rt) \]
where:
- \( A \) = the total amount (principal + interest)
- \( P \) = principal amount ($4,300)
- \( r \) = rate of interest (as a decimal) (7.5% = 0.075)
- \( t \) = time in years (2 years)
Substituting the values:
\[ A = 4300(1 + 0.075 \times 2) = 4300(1 + 0.15) = 4300 \times 1.15 \]
\[ A = 4300 \times 1.15 = 4945 \]
So, the total amount with simple interest after 2 years is $4,945.
Compound Interest Calculation
The formula for compound interest is:
\[ A = P(1 + r)^t \]
where:
- \( A \) = the total amount (principal + interest)
- \( P \) = principal amount ($4,300)
- \( r \) = rate of interest (as a decimal) (7% = 0.07)
- \( t \) = time in years (2 years)
Substituting the values:
\[ A = 4300(1 + 0.07)^2 = 4300(1.07)^2 \]
Calculating \( (1.07)^2 \):
\[ (1.07)^2 = 1.1449 \]
Now, substituting this back:
\[ A = 4300 \times 1.1449 \approx 4924.27 \]
So, the total amount with compound interest after 2 years is approximately $4,924.27.
Comparison
- Simple Interest Total: $4,945
- Compound Interest Total: $4,924.27
Conclusion
Simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment, compared to compound interest at 7.0% which results in about $4,924.27.
Therefore, the correct response is: Simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment.