Question

You currently have $6,800 (Present Value) in an account that has an interest rate of 7% per year compounded daily (365 times per year). You want to withdraw all your money when it reaches $12,240 (Future Value). In how many years will you be able to withdraw all your money? The number of years is . Round your answer to 1 decimal place.

Answer 1

To find out how many years it will take for your money to reach $12,240, we can use the formula for compound interest:

Future Value = Present Value * (1 + interest rate / number of compounding periods)^(number of compounding periods * number of years)

In this case, the Present Value is $6,800, the Future Value is $12,240, and the interest rate is 7%. The compounding is done daily, so the number of compounding periods per year is 365.

Let's solve the equation:

12,240 = 6,800 * (1 + 0.07 / 365)^(365 * number of years)

To make the calculation easier, let's simplify the equation:

1.8 = (1 + 0.07 / 365)^(365 * number of years)

Now, let's take the natural logarithm of both sides to solve for the number of years:

ln(1.8) = ln((1 + 0.07 / 365)^(365 * number of years))

Using logarithmic properties, we can simplify further:

ln(1.8) = (365 * number of years) * ln(1 + 0.07 / 365)

Now, let's solve for the number of years by dividing both sides of the equation by (365 * ln(1 + 0.07 / 365)):

number of years = ln(1.8) / (365 * ln(1 + 0.07 / 365))

Using a calculator, we can find the value of ln(1.8) to be approximately 0.5878. Plugging this value into the equation, we get:

number of years = 0.5878 / (365 * ln(1 + 0.07 / 365))

After evaluating this expression, we find that the number of years is approximately 5.9. Rounding this to 1 decimal place, we can conclude that it will take approximately 5.9 years for your money to reach $12,240.

Therefore, you will be able to withdraw all your money in approximately 5.9 years.

Explanation:

<3