Final answer:
To determine the number of months it will take for the checking account to have the same amount of money as the savings account, we can use the formula for compound interest. By plugging in the given values and solving for time, we can find the solution. The final step is to divide the time by 12 to get the number of months.
Step-by-step explanation:
To determine how many months it will take for the checking account to have the same amount of money as the savings account, we need to consider the interest rate on each account. Let's assume the checking account has a balance of $x and the savings account has a balance of $10,000. If the checking account pays 10% interest compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the ending balance
- P is the initial balance
- r is the interest rate (in decimal form)
- n is the number of times interest is compounded per year
- t is the time in years
In this case, we want to find the time it takes for the checking account to reach $10,000, so A = $10,000, P = $x, r = 0.10, n = 1 (compounded annually), and t is the unknown number of years. Plugging these values into the formula, we get:
$10,000 = $x(1 + 0.10/1)^(1t)
Since the interest is compounded annually, the equation simplifies to:
$10,000 = $x(1 + 0.10)^t
Now, we can solve for t by dividing both sides of the equation by $x and taking the logarithm of both sides:
log(($10,000/$x)) = log((1 + 0.10)^t)
t = log(($10,000/$x)) / log((1 + 0.10))
We want to find the number of months, so we need to divide t by 12:
Number of months = t / 12
Now we can calculate the number of months it will take for the checking account to have the same amount of money as the savings account.