Answer:
P ≈ $12,654.89
Explanation:
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 in this case)
P = the principal amount (the amount to be deposited today)
r = the annual interest rate (4.5% or 0.045 as a decimal)
n = the number of times the interest is compounded per year (monthly compounding, so n = 12)
t = the number of years (4 years in this case)
Substituting the given values into the formula, we have:
$15,000 = P(1 + 0.045/12)^(12*4)
Simplifying the equation:
$15,000 = P(1.00375)^(48)
To solve for P, we divide both sides of the equation by (1.00375)^(48):
P = $15,000 / (1.00375)^(48)
Using a calculator, we find:
P ≈ $12,654.89
Therefore, approximately $12,654.89 should be deposited today in order to accumulate to $15,000 in 4 years with a 4.5% annual interest rate compounded monthly.