Question

compounded hourly is birr 1000 at 6% for 10 years?

Answer 1

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:

1. Calculate \(\frac{0.06}{8760}\):
\[
\frac{0.06}{8760} \approx 0.00000684
\]

2. Calculate \(n \times t = 8760 \times 10 = 87600\).

3. Now compute \(A\):
\[
A = 1000 \left(1 + 0.00000684\right)^{87600}
\]

4. Calculate \(1 + 0.00000684\):
\[
1 + 0.00000684 \approx 1.00000684
\]

5. 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**.