Suppose you won a contest at 9th grade start that deposited $3,000 in an account that pays 5% annual interest compounded continuously. You go to college for four years (four years later). How much will you have then?
To determine how much you will have in your account after four years, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = The final amount
P = The initial principal (the amount deposited at the beginning)
e = Euler's number (approximately 2.71828)
r = The interest rate per time period (in this case, the annual interest rate)
t = Number of time periods elapsed (in this case, four years)
Given:
P = $3,000
r = 5% = 0.05
t = 4 years
Using the formula, we can calculate the final amount as follows:
A = 3000 * e^(0.05*4)
Now, let's solve it step by step:
1. Calculate the exponential part first:
e^(0.05*4) = 2.71828^(0.05*4)
2. Multiply the calculated exponential value with the initial principal:
A = 3000 * (e^(0.05*4))
Let's use a calculator or a programming language to calculate the value of e^(0.05*4).
A ≈ 3000 * (2.71828^(0.2))
A ≈ 3000 * 1.221402758
Calculating the final value:
A ≈ $3,664.21
Therefore, after four years, you will have approximately $3,664.21 in your account.