Suppose $15000 is invested in an account for 6 years. Find the balance in the account if interest is compounded continuously at 6%.
what is
15000(e^(.06(6)) ?
i got 21499.94
To find the balance in the account if interest is compounded continuously at 6%, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the future balance after time t
P = the principal amount (initial investment)
e = the mathematical constant approximately equal to 2.71828
r = the annual interest rate (in decimal form)
t = the number of years
In this case, the principal amount (P) is $15000, the interest rate (r) is 6% or 0.06, and the time period (t) is 6 years.
Plugging in the values into the formula, we get:
A = 15000 * e^(0.06 * 6)
Now, let's calculate the value of e^(0.06 * 6):
e^(0.36) ≈ 1.4349
Substituting this value back into the main formula, we have:
A ≈ 15000 * 1.4349
Calculating this, we get:
A ≈ $21,523.50
Therefore, the balance in the account after 6 years with continuous compounding at 6% interest is approximately $21,523.50.
To find the balance in the account with continuous compounding, we can use the formula for compound interest:
A = P * e^(rt)
Where:
A = future balance
P = initial principal (investment)
e = Euler's number (approximately 2.71828)
r = interest rate
t = time (in years)
Given:
P = $15000
r = 6% = 0.06
t = 6 years
Substituting these values into the formula, we have:
A = 15000 * e^(0.06 * 6)
Now, let's calculate it step by step:
Step 1: Multiply the interest rate (r) by the time period (t)
0.06 * 6 = 0.36
Step 2: Multiply the result by the initial principal (P)
15000 * 0.36 = 5400
Step 3: Find the value of e^(0.36)
Using a calculator, the approximate value of e^(0.36) is 1.43508
Step 4: Multiply the result from step 2 by the result from step 3
5400 * 1.43508 = 7744.44 (rounded to two decimal places)
Therefore, the balance in the account after 6 years with continuous compounding at 6% is approximately $7744.44.