Question

You currently have $600 (Present Value) in an account that has an interest rate of 4% per year compounded daily (365 times per year). You want to withdraw all your money when it reaches $1,440 (Future Value). In how many years will you be able to withdraw all your money?

Answer 1

To find out how many years it will take for $600 to grow to $1,440 with a 4% interest rate compounded daily, you use the compound interest formula and solve for time. Using the values provided and a calculator, you'd be able to calculate the exact number of years needed for the account to reach the desired future value.

Step-by-step explanation:

You're asking how many years it will take for $600 in an account with a 4% annual interest rate compounded daily to grow to $1,440. The formula for compound interest that we can use is A = P(1 + r/n)^(nt), 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 (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested or borrowed for, in years.

To calculate the number of years (t), we rearrange the formula to solve for t, which gives us t = ln(A/P) / (n * ln(1 + r/n)). Plugging in the given values, we plug A = $1,440, P = $600, r = 0.04 (since 4% is 0.04 as a decimal), and n = 365 into that equation. We can then solve for t using a calculator.