To determine which interest earning type will result in a higher balance when $4,300 is invested for 2 years at the given interest rates, we can calculate the balances for both simple interest and compound interest.
Simple Interest Calculation
The formula for simple interest is: \[ \text{Total Amount} = P + (P \times r \times t) \] where:
- \( P \) = principal amount ($4,300)
- \( r \) = interest rate (7.5% or 0.075)
- \( t \) = time in years (2)
Calculating the simple interest: \[ \text{Simple Interest} = 4300 \times 0.075 \times 2 = 645 \] Adding this interest to the principal: \[ \text{Total Amount} = 4300 + 645 = 4945 \]
Compound Interest Calculation
The formula for compound interest is: \[ A = P \left(1 + r\right)^t \] where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = principal amount ($4,300)
- \( r \) = annual interest rate (7% or 0.07)
- \( t \) = number of years the money is invested (2)
Calculating the compound interest: \[ A = 4300 \left(1 + 0.07\right)^2 = 4300 \left(1.07\right)^2 = 4300 \times 1.1449 \approx 4914.07 \]
Conclusion
Now we can compare the two results:
- Simple Interest Balance: $4,945
- Compound Interest Balance: $4,914.07
Thus, simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment. The correct response from your options is:
Simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment.