Question

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

Answer 1

To calculate the future value of an investment compounded continuously, you can use the formula:

\[
A = Pe^{rt}
\]

Where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (decimal).
- \(t\) is the time the money is invested for in years.
- \(e\) is the base of the natural logarithm (approximately equal to 2.71828).

Given:
- \(P = 1000\) birr
- \(r = 0.06\) (6%)
- \(t = 10\) years

Now plug in the values:

\[
A = 1000 \cdot e^{0.06 \cdot 10}
\]
\[
A = 1000 \cdot e^{0.6}
\]

Using the value of \(e^{0.6} \approx 1.8221\):

\[
A \approx 1000 \cdot 1.8221 \approx 1822.10
\]

So, after 10 years, the amount will be approximately **1822.10 birr** when compounded continuously at a rate of 6%.