find the balance after 15 years of a $2500 investment earning 5.5% interest compounded continuously
Someone show me how to do this, please?!
P = Po*e^rt.
r = 0.055 = APR expressed as decimal.
t = 15 Years.
rt = 0.055*15 = 0.825.
P = 2500*e^0.825 = $5704.70.
Thanks to this Question thankyou
To find the balance after 15 years of a $2500 investment earning 5.5% interest compounded continuously, you can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the balance after the given time
P = the principal amount (initial investment)
e = the mathematical constant approximately equal to 2.71828
r = the interest rate per year (as a decimal)
t = the time in years
In this case, the principal amount (P) is $2500, the interest rate (r) is 5.5% (or 0.055 as a decimal), and the time (t) is 15 years. Now, let's plug these values into the formula:
A = 2500 * e^(0.055 * 15)
To calculate the result, we need to use the value of e raised to the power of (0.055 multiplied by 15). The result is approximately 6658.07.
Therefore, the balance after 15 years of a $2500 investment earning 5.5% interest compounded continuously is approximately $6658.07.
To find the balance after 15 years of a $2500 investment earning 5.5% interest compounded continuously, you can use the formula for continuous compound interest. The formula is:
A = P * e^(rt)
Where:
A is the final balance
P is the principal amount (initial investment)
e is the mathematical constant approximately equal to 2.71828
r is the interest rate (in decimal form)
t is the time period (in years)
In this case, P = $2500, r = 5.5% (or 0.055 as a decimal), and t = 15.
Now we can substitute these values into the formula:
A = 2500 * e^(0.055 * 15)
To evaluate this expression, we need to find the value of e^(0.055 * 15). You can use a scientific calculator or an online calculator to calculate this.
Using a calculator, we find:
e^(0.055 * 15) ≈ 2.9300290405
Now we can substitute this value back into the formula:
A ≈ 2500 * 2.9300290405
A ≈ $7,325.07
Therefore, the balance after 15 years of a $2500 investment earning 5.5% interest compounded continuously is approximately $7,325.07.