How much would you need to deposit in an account each month in order to have $20,000 in the account in 10 years? Assume the account earns 4% interest.

To solve this problem, we need to use the formula for the future value of a series of payments, or an annuity. This formula is:

FV = P * [(1 + r/n)^(nt) - 1] / (r/n)

where: FV = future value of the annuity (the amount you want to have saved) P = payment amount (the amount you deposit each month) r = annual interest rate (in decimal form) n = number of times the interest is compounded per year t = number of years

In this case, you want to solve for P (the monthly deposit), so you need to rearrange the formula to solve for P:

P = FV * (r/n) / [(1 + r/n)^(nt) - 1]

You're given: FV = $20,000 r = 4% = 0.04 n = 12 (since interest is compounded monthly) t = 10 years

Substitute these values into the formula:

P = $20,000 * (0.04/12) / [(1 + 0.04/12)^(12*10) - 1]

Now, calculate the value inside the brackets:

= $20,000 * (0.003333) / [(1.003333)^(120) - 1]

= $20,000 * 0.003333 / [3.2434 - 1]

= $20,000 * 0.003333 / 2.2434

Finally, calculate P:

P = $29.73

So, you would need to deposit approximately $29.73 each month in order to have$20,000 in the account in 10 years, assuming the account earns 4% interest.