To determine which type of interest will result in a higher balance after 2 years with the given investment, we need to calculate both the simple interest and the compound interest.
Simple Interest Calculation
The formula for calculating simple interest is:
\[ A = P(1 + rt) \]
Where:
- \(A\) = the total amount of money after interest
- \(P\) = the principal amount (initial investment)
- \(r\) = the annual interest rate (in decimal form)
- \(t\) = the time in years
Given:
- \(P = 4300\)
- \(r = 7.5% = 0.075\)
- \(t = 2\)
Substituting the values into the formula:
\[ A = 4300(1 + 0.075 \cdot 2) = 4300(1 + 0.15) = 4300 \cdot 1.15 = 4945 \]
Compound Interest Calculation
The formula for calculating compound interest is:
\[ A = P(1 + r)^t \]
Where:
- \(A\) = the total amount of money after interest
- \(P\) = the principal amount (initial investment)
- \(r\) = the annual interest rate (in decimal form)
- \(t\) = the number of compounding periods (in years)
Given:
- \(P = 4300\)
- \(r = 7.0% = 0.07\)
- \(t = 2\)
Substituting the values into the formula:
\[ A = 4300(1 + 0.07)^2 = 4300(1.07)^2 = 4300 \cdot 1.1449 \approx 4922.07 \]
Summary of Resuts:
- Simple Interest Balance after 2 years: $4,945
- Compound Interest Balance after 2 years: $4,922.07
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 approximately $4,922.07.
The correct response is: Simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment.