To determine which interest earning type offers more financial gains after 1 year, we need to calculate both the simple interest and the compound interest for the given investment of $750.
Simple Interest Calculation
The formula for simple interest is:
\[ \text{Simple Interest} = P \times r \times t \]
Where:
- \( P \) = principal amount ($750)
- \( r \) = rate of interest (3% or 0.03)
- \( t \) = time in years (1)
\[ \text{Simple Interest} = 750 \times 0.03 \times 1 = 22.50 \]
Therefore, the simple interest after 1 year is $22.50.
Compound Interest Calculation
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = principal amount ($750)
- \( r \) = annual interest rate (2% or 0.02)
- \( n \) = number of times that interest is compounded per year (monthly, so \( n = 12 \))
- \( t \) = time in years (1)
Calculating it step by step:
-
Calculate the monthly interest rate: \[ \frac{r}{n} = \frac{0.02}{12} = 0.00166667 \]
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Calculate the total number of compounding periods: \[ nt = 12 \times 1 = 12 \]
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Plugging these values into the compound interest formula: \[ A = 750 \left(1 + 0.00166667\right)^{12} \] \[ A = 750 \left(1.00166667\right)^{12} \] \[ A \approx 750 \left(1.02018885991584\right) \approx 765.14 \]
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Now subtract the principal to find the compound interest: \[ \text{Compound Interest} = A - P = 765.14 - 750 \approx 15.14 \]
Conclusion
- Simple interest after 1 year: $22.50
- Compound interest after 1 year: $15.14
So, simple interest at 3% offers more financial gains after 1 year compared to compound interest at 2%.
Therefore, the correct response is:
Simple interest at 3% offers more financial gains.