To calculate the interest income earned on Ato XX's deposit of Birr 200,000 at a 12% annual interest rate compounded monthly, we follow these steps:
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Calculate the total amount in the account after 2 years with monthly compounding: 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.
- \( P \) = the principal amount (the initial deposit or investment).
- \( r \) = 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
- \( r = 12% = 0.12 \)
- \( n = 12 \) (monthly compounding)
- \( t = 2 \)
Plugging these values into the formula:
\[ A = 200,000 \left(1 + \frac{0.12}{12}\right)^{12 \times 2} \]
\[ A = 200,000 \left(1 + 0.01\right)^{24} \]
\[ A = 200,000 \left(1.01\right)^{24} \]
Now calculate \( (1.01)^{24} \):
\[ (1.01)^{24} \approx 1.268241 \]
Now, substitute this back into the equation for \( A \):
\[ A = 200,000 \times 1.268241 \approx 253,648.20 \]
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Calculate the interest earned: The interest earned is:
\[ \text{Interest} = A - P \]
\[ \text{Interest} = 253,648.20 - 200,000 = 53,648.20 \]
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Calculate the interest income tax: If we assume the tax rate on interest income is a specific percentage (which is normally specified by tax regulations), we can calculate the tax. For example, if the tax rate is 10%, the interest income tax would be:
\[ \text{Tax} = \text{Interest} \times \text{Tax Rate} \]
\[ \text{Tax} = 53,648.20 \times 0.10 = 5,364.82 \]
You would need to confirm the applicable tax rate on interest income to find the specific amount of tax.
Summary:
- Total amount after 2 years: Approximately 253,648.20 Birr
- Interest earned: Approximately 53,648.20 Birr
- Tax on interest income (using a hypothetical tax rate of 10%): Approximately 5,364.82 Birr
Please verify the tax rate applicable to Ato XX for a precise calculation.