To calculate the interest earned on the deposit over two years with monthly compounding, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = the future value of the investment/loan, including interest
- \( P \) = the principal investment amount (the initial deposit or loan amount)
- \( r \) = the annual interest rate (decimal)
- \( n \) = the number of times that interest is compounded per year
- \( t \) = the number of years the money is invested or borrowed
Given:
- \( P = 200,000 \) Birr
- \( r = 0.12 \) (12% annual interest rate)
- \( n = 12 \) (interest is compounded monthly)
- \( t = 2 \) years
Now, substitute the values into the formula:
\[ A = 200,000 \left(1 + \frac{0.12}{12}\right)^{12 \cdot 2} \]
Calculate \( \frac{0.12}{12} = 0.01 \):
\[ A = 200,000 \left(1 + 0.01\right)^{24} \]
This simplifies to:
\[ A = 200,000 \left(1.01\right)^{24} \]
Now calculate \( \left(1.01\right)^{24} \):
\[ (1.01)^{24} \approx 1.2682418 \]
Now substitute back into the equation:
\[ A \approx 200,000 \cdot 1.2682418 \approx 253648.36 \]
The total amount after two years is approximately 253,648.36 Birr.
Now calculate the interest earned:
\[ \text{Interest} = A - P = 253648.36 - 200000 \approx 53648.36 \text{ Birr} \]
To find the tax on the interest income, we need to know the tax rate applicable. Assuming there is no specific tax rate provided, we cannot calculate tax without this information.
If you provide the applicable tax rate or percentage for interest income, I can help you calculate the amount of tax owed on that interest income. Otherwise, the interest income is approximately 53,648.36 Birr.