find the accumulated value of an investment of 5000 at 9% compounded continuously for 6 years.
Amount = 5000(e)^(.09x6)
= 5000(e^.54)
= 8580.03
your general formula is
Amount = Principal(e)rt where r is the annual rate and t is the number of years.
I don't understand what it is exaclty you multiply to get 8580.03. Please respond back. I need to understand this. Because when I multiply 5000x.54 I don't get that.
I am using the exponential function e^x
it is the inverse function of ln on your calculator.
The nature of the question requires you to know about exponential functions.
On my calculator I press
2nd F (ln)
.54
=
to get 1.7160068...
To find the accumulated value of an investment compounded continuously, we can use the formula:
A = Pe^rt
Where:
A is the accumulated value of the investment
P is the principal amount (initial investment)
e is Euler's number (approximately 2.71828)
r is the annual interest rate
t is the time in years
In this case:
P = $5000
r = 9% (or 0.09 as a decimal)
t = 6 years
Substituting these values into the formula, we can calculate the accumulated value:
A = 5000 * e^(0.09 * 6)
Now, let's calculate it step by step.
First, multiply the interest rate and the time:
0.09 * 6 = 0.54
Next, calculate e^0.54 using Euler's number:
e^0.54 ≈ 1.718 (rounded to three decimal places)
Finally, multiply the principal amount by the result:
5000 * 1.718 = $8,590
Therefore, the accumulated value of the investment after 6 years, compounded continuously at 9%, is approximately $8,590.