Question

$5000 is invested in an account where interest is compounded continuosuly at 6%interest how much money will be in the account after 15 years

Answer 1

To calculate the amount of money in the account after 15 years with continuous compounding interest, you can use the formula for compound interest in continuous compounding:

A = P * e^(rt)

Where:
A = the future amount
P = the principal amount (initial investment) = $5000
r = annual interest rate (as a decimal) = 6% or 0.06
t = time in years = 15
e = Euler's number, approximately equal to 2.71828

Now, plug in the values:

A = 5000 * e^(0.06 * 15)

A ≈ 5000 * e^(0.9)

A ≈ 5000 * 2.4596 (rounded to four decimal places)

A ≈ $12,298

So, after 15 years with continuous compounding interest at a rate of 6%, there will be approximately $12,298 in the account.