find an accumulated value of investment of $5000 at 9%compound continuously for 6 years.
Use formula A=P(1+r/n)^nt and A=Pe^rt
To find the accumulated value of an investment using compound interest continuously, we can use the formula:
A = Pe^(rt)
Where:
A is the accumulated value or final amount
P is the principal or initial investment amount
r is the interest rate expressed in decimal form
t is the time period in years
In this case, the principal (P) is $5000 and the interest rate (r) is 9% or 0.09 in decimal form. The time period (t) is 6 years.
Now, we can calculate the accumulated value:
A = 5000e^(0.09*6)
First, we calculate the exponent: 0.09 multiplied by 6, resulting in 0.54.
Next, we find e^(0.54) using a scientific calculator or an online calculator. The value of e is approximately 2.71828.
A = 5000 * 2.71828^(0.54)
Multiplying and raising 2.71828 by 0.54 will give you the final result.
After performing this calculation, the accumulated value of the investment after 6 years with continuous compound interest at a rate of 9% will be approximately $7610.62.