An account offers an APR of 6% compounded monthly. How much must you deposit today into this account in order to have $10,000 in five years.

P = Po(1+r)^n.

P = $10,000.

Po = Initial deposit = ?.

r = 0.06/12 = 0.005 = Monthly % rate.

n = 12Comp./yr. * 5yrs. = 60 Compounding periods.

To determine how much you need to deposit today in order to have $10,000 in five years with an APR of 6% compounded monthly, you can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment ($10,000 in this case)
P = the principal amount (the amount you need to deposit today)
r = annual interest rate (6% or 0.06 in decimal form)
n = number of times interest is compounded per year (monthly, so 12)
t = number of years (5)

Plugging in the values, the formula becomes:

10,000 = P(1 + 0.06/12)^(12*5)

Now you need to solve for P. Here's how you can do it step-by-step:

Step 1: Simplify the fraction inside the parentheses:
10,000 = P(1 + 0.005)^(60)

Step 2: Add 1 to 0.005:
10,000 = P(1.005)^(60)

Step 3: Calculate the value inside the parentheses:
(1.005)^(60) ≈ 1.3382

Step 4: Divide both sides of the equation by 1.3382:
10,000 / 1.3382 ≈ P

Step 5: Round the result to the nearest cent:
P ≈ $7,479.85

Therefore, you would need to deposit approximately $7,479.85 today into this account in order to have $10,000 in five years with an APR of 6% compounded monthly.