To find the difference in financial gains between simple interest and compound interest for the given investment, we need to calculate both types of interest and then find the difference.
1. Simple Interest (SI)
The formula for simple interest is: \[ \text{SI} = P \times r \times t \] where:
- \(P = 3200\) (principal amount),
- \(r = 0.045\) (interest rate),
- \(t = 8\) (time in years).
Calculating: \[ \text{SI} = 3200 \times 0.045 \times 8 = 3200 \times 0.36 = 1152 \]
Total amount with simple interest: \[ \text{Total SI} = P + \text{SI} = 3200 + 1152 = 4352 \]
2. Compound Interest (CI)
The formula for compound interest is: \[ \text{CI} = P \times (1 + r)^t - P \]
Calculating: \[ \text{CI} = 3200 \times (1 + 0.045)^8 - 3200 \]
Calculating \((1 + 0.045)^8\): \[ (1.045)^8 \approx 1.432364654 \] Now we can calculate the CI: \[ \text{CI} = 3200 \times 1.432364654 - 3200 \] \[ \text{CI} \approx 4583.4 - 3200 = 1383.4 \]
3. Difference in Gains: \[ \text{Difference} = \text{CI} - \text{SI} = 1383.4 - 1152 = 231.4 \]
Thus, the difference in financial gains from the two methods of calculating interest is approximately $231.4. Since it closely matches one of the answer choices:
- $231.57
So, the correct response is $231.57.
1 answer