To compare simple interest and compound interest, we will use the formulas for each type of interest.
1. Calculate Simple Interest:
The formula for simple interest (SI) is: \[ SI = P \times r \times t \] where:
- \( P \) is the principal amount ($4,300),
- \( r \) is the rate (7.5% or 0.075),
- \( t \) is the time in years (2 years).
Substituting the values: \[ SI = 4300 \times 0.075 \times 2 = 4300 \times 0.15 = 645 \] The total balance after 2 years with simple interest is: \[ Total , Balance = P + SI = 4300 + 645 = 4945 \]
2. Calculate Compound Interest:
The formula for compound interest (CI) is: \[ A = P \times (1 + r)^t \] where:
- \( P \) is the principal amount ($4,300),
- \( r \) is the rate (7.0% or 0.07),
- \( t \) is the time in years (2 years).
Substituting the values into the formula: \[ A = 4300 \times (1 + 0.07)^2 = 4300 \times (1.07)^2 \] Calculating \( (1.07)^2 \): \[ (1.07)^2 = 1.1449 \quad (\text{approximately}) \] Now calculating the total balance: \[ A = 4300 \times 1.1449 \approx 4924.67 \]
Summary:
- Simple Interest total balance after 2 years = $4,945
- Compound Interest total balance after 2 years = approximately $4,924.67
Based on this calculation, simple interest at 7.5% results in a higher balance of $4,945 after 2 years of investment.