To find the amount A in an account after t years with principal P and an annual interest rate r compounded continuously, you can use the formula
A=Pe^rt, is right, but can you help mw with this question.
Find the amount A in an account after t years if dA/dt=rA
A(0)=5,000 and A(5)=5,282.70
To find the amount A in an account after t years with principal P and an annual interest rate r compounded continuously, you can use the formula:
A = P * e^(rt)
where:
A = the amount in the account after t years
P = the principal (initial amount of money)
r = the annual interest rate (in decimal form)
t = the number of years
e = Euler's number (approximately 2.71828)
By substituting the values of P, r, and t into the formula, you can calculate the amount A in the account after t years.
The formula to find the amount A in an account after t years with principal P and an annual interest rate r compounded continuously is:
A = P * e^(rt)
Here's how to use the formula:
1. Start with the given principal amount, P.
2. Determine the annual interest rate, r, for the account. Make sure it is in decimal form (e.g., 5% would be written as 0.05).
3. Decide on the time period in years, t, for which you want to calculate the amount.
4. Calculate the value e^(rt), where e is Euler's number, approximately 2.71828. This is the exponential function e to the power of (rt). Use either a scientific calculator or the exponential function on a calculator (e.g., Excel).
5. Multiply the principal, P, by the result from step 4 to get the amount, A.
6. Round the answer to the desired number of decimal places, if necessary.
Note: The formula assumes continuous compounding, which means the interest is applied continuously throughout the year. This is different from other compounding periods, such as annually, semi-annually, quarterly, or monthly.