Question

$250 is left in a savings account at 4% interest, and the interest is compounded continuously. If the balance is now $330.78, then how many years was the money in the account?

Answer 1

The formula for continuous compound interest is A = P * e^(rt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (converted to decimal form)
- t is the time the money is invested for, in years.

For this problem, we know that the initial amount P is $250, the final amount A is $330.78, and the annual interest rate r is 4% or 0.04 in decimal. We want to find t, the time the money was in the account.

First, we should manipulate our formula to solve for t. To isolate t, we can divide both sides by P * e^(rt) and then take the logarithm ln:

t = ln(A / P) / r

Now we can substitute the given values into our new equation:

t = ln(330.78 / 250) / 0.04
t ≈ 7 years.

So, the money was in the account for approximately 7 years.