To calculate the amount of interest income tax on Ato XX's deposit, we first need to find out how much interest has been earned on the deposit over the two years at the rate of 12% compounded monthly.
Step 1: Calculate the total amount in the account after 2 years
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \(A\) = the future value of the investment/loan, including interest
- \(P\) = the principal investment amount (initial deposit)
- \(r\) = annual interest rate (decimal)
- \(n\) = number of times that interest is compounded per year
- \(t\) = the number of years the money is invested or borrowed
Substituting the values we have:
- \(P = 200,000\) Birr
- \(r = 0.12\) (12%)
- \(n = 12\) (monthly compounding)
- \(t = 2\) years
Calculating it:
\[ A = 200,000 \left(1 + \frac{0.12}{12}\right)^{12 \times 2} \] \[ A = 200,000 \left(1 + 0.01\right)^{24} \] \[ A = 200,000 \left(1.01\right)^{24} \]
Now, calculate \((1.01)^{24}\):
\[ (1.01)^{24} \approx 1.268241795 \]
Continuing with the calculation:
\[ A \approx 200,000 \times 1.268241795 \approx 253,648.36 \]
Step 2: Calculate the interest earned
The interest earned can be calculated as:
\[ \text{Interest} = A - P \]
Substituting the values:
\[ \text{Interest} = 253,648.36 - 200,000 \approx 53,648.36 \]
Step 3: Calculate the interest income tax
To find the tax on the interest earned, we need to know the tax rate applicable. Assuming there is a specific income tax rate on interest (which varies by jurisdiction), let’s say the income tax rate on interest is 10% (you would need to adjust this based on actual applicable rates).
Calculating the tax:
\[ \text{Interest Income Tax} = \text{Interest} \times \text{Tax Rate} \]
Substituting the values:
\[ \text{Interest Income Tax} = 53,648.36 \times 0.10 \approx 5,364.84 \]
Conclusion
If the tax rate on the interest is assumed to be 10%, the amount of interest income tax on the deposit after two years would be approximately Birr 5,364.84. Adjust according to the actual applicable tax rate if different.