To calculate the future value of an investment compounded hourly, you can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \(A\) = the amount of money accumulated after n years, including interest.
- \(P\) = the principal amount (the initial amount of money, which is 1000 Birr).
- \(r\) = the annual interest rate (decimal) (6%, or 0.06).
- \(n\) = the number of times that interest is compounded per year (for hourly compounding, this would be 24 hours/day × 365 days/year = 8760).
- \(t\) = the number of years the money is invested or borrowed (10 years).
Now, substituting the values into the formula:
\[ P = 1000 \] \[ r = 0.06 \] \[ n = 8760 \] \[ t = 10 \]
\[ A = 1000 \left(1 + \frac{0.06}{8760}\right)^{8760 \times 10} \]
Calculating the value step-by-step:
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Calculate \(\frac{0.06}{8760}\): \[ \frac{0.06}{8760} \approx 0.00000684 \]
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Calculate \(n \times t = 8760 \times 10 = 87600\).
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Now compute \(A\): \[ A = 1000 \left(1 + 0.00000684\right)^{87600} \]
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Calculate \(1 + 0.00000684\): \[ 1 + 0.00000684 \approx 1.00000684 \]
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Raise it to the power of 87600: \[ A \approx 1000 \left(1.00000684\right)^{87600} \]
Using a calculator to compute \(A\):
\[ A \approx 1000 \times e^{0.06} \approx 1000 \times 1.061677812 \] \[ A \approx 1061.68 \]
So, after 10 years, if you invest 1000 Birr at a 6% annual interest rate compounded hourly, the amount will be approximately 1061.68 Birr.