Question

compounded daily is investment birr 1000 at 6% for 10 years?

Answer 1

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**.