If $6,000 is placed in an account with an annual interest rate of 3%, how long will it take the amount to triple if the interest is compounded annually?

To find out how long it will take for the amount to triple, we need to determine the number of compounding periods required. We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:
A = the final amount
P = the initial principal (in this case, $6,000)
r = annual interest rate (in this case, 3% or 0.03)
n = number of times interest is compounded per year (in this case, once annually)
t = number of years

Since we want to triple the amount, the final amount A will be 3 times the initial principal P:

3P = P(1 + r/n)^(nt)

Now we can solve for t by isolating it:

3 = (1 + r/n)^(nt)

Taking the logarithm of both sides will help us solve for t:

log(3) = log((1 + r/n)^(nt))

Using the logarithmic property log(a^b) = b * log(a), we simplify further:

log(3) = nt * log(1 + r/n)

Finally, we can solve for t:

t = (1/n) * log(3) / log(1 + r/n)

Plugging in the values:

t = (1/1) * log(3) / log(1 + 0.03/1)

Using a calculator, we find:

t ≈ (log(3) / log(1.03)) ≈ 22.48

Therefore, it will take approximately 22.48 years for the amount to triple if the interest is compounded annually.