To calculate the amount of money that should be deposited today, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($15,000)
P = the principal amount (the amount to be deposited today, which we are trying to find)
r = the annual interest rate (3.5% or 0.035 as a decimal)
n = the number of times interest is compounded per year (monthly, so n = 12)
t = the number of years (3 years)
Plugging in the values into the formula, we have:
$15,000 = P(1 + 0.035/12)^(12*3)
Simplifying further:
$15,000 = P(1.0029167)^(36)
Now, we can isolate P by dividing both sides of the equation by (1.0029167)^(36):
P = $15,000 / (1.0029167)^(36)
Using a calculator, we find:
P ≈ $13,019.74
Therefore, approximately $13,019.74 should be deposited today in order to accumulate to $15,000 in 3 years with a monthly interest rate of 3.5%.