2000 dollars is invested in a bank account at an interest rate of 8 percent per year, compounded continuously. meanwhile, 11000 dollars is invested in a bank account at an interest rate of 4 percent compounded annually. to the nearest year, when will the two accounts have the same balance? the two accounts will have the same balance after .

The two accounts will have the same balance after 41.8 years

Explanation:

Hi, first, let´s intruduce the mathematical expression for the future value of each investment.

$2,000 compounded continously

$11,000 at 4% compounded annually (equivalent to effective annual)

Since the problem is asking when the future value of both investment will reach an equal amount of money, we solve for "t" the resulting expression:

So, this 2 accounts will need 41.8 years to equal their balance. You can check your result by substituting "t" in both equations, they must have the same future value.

Best of luck.