To find out how long it takes for a deposit to grow to a certain amount, use the compound interest formula. For a deposit of $3,500 growing to $6,500 at a monthly interest rate of 0.52%, the equation is $6,500 = $3,500(1 + 0.0052/12)^12t, which you can solve for time, t, using logarithmic functions.
To calculate how long it takes for a deposit to grow to a certain amount with compound interest, you can use the formula for compound interest:
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.
t is the time the money is invested or borrowed for, in years.
In your case:
A is $6,500 (the desired amount).
P is $3,500 (your initial deposit).
r is 0.0052, as the monthly interest rate is 0.52% (0.52/100 to convert percentage to a decimal).
n is 12, since the interest is compounded monthly.
t is what we're solving for.
First, you'll need to set up the equation based on the information provided:
$6,500 = $3,500(1 + 0.0052/12)12t
Then, you can solve for t:
t = ln($6,500 / $3,500) / (12 * ln(1 + 0.0052/12))
Calculating this gives you the number of years you need to wait until your account has grown to $6,500.
You would use a calculator for this step and ensure you round your answer to two decimal places as directed.