To calculate the future value of an investment compounded daily, 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).
- \(r\) = 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.
In this case:
- \(P = 1000\) birr
- \(r = 6% = 0.06\)
- \(n = 365\) (daily compounding)
- \(t = 10\)
Now plug in the values:
\[ A = 1000 \left(1 + \frac{0.06}{365}\right)^{365 \times 10} \]
\[ A = 1000 \left(1 + \frac{0.06}{365}\right)^{3650} \]
Calculating \( \frac{0.06}{365} \):
\[ \frac{0.06}{365} \approx 0.000164384 \]
Now calculate \(1 + \frac{0.06}{365}\):
\[ 1 + 0.000164384 \approx 1.000164384 \]
Now raise that to the power of \(3650\):
\[ A \approx 1000 \times (1.000164384)^{3650} \]
Using a calculator, you find:
\[ A \approx 1000 \times 1.7137 \approx 1713.70 \]
Therefore, the future value of the investment after 10 years, compounded daily at an interest rate of 6%, would be approximately 1713.70 birr.
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