Answer:
To calculate the amount of money that should be deposited today to accumulate $12,000 in three years with a 4% interest rate compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (desired value) = $12,000
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal) = 4% = 0.04
n = Number of times interest is compounded per year = 12 (monthly compounding)
t = Number of years = 3
Substituting these values into the formula, we have:
$12,000 = P(1 + 0.04/12)^(12×3)
Simplifying the equation:
$12,000 = P(1.00333333333)^(36)
Now, let's solve for P:
P = $12,000 / (1.00333333333)^36
Using a calculator, we find:
P ≈ $10,657.01
Therefore, approximately $10,657.01 should be deposited today in order to accumulate $12,000 in three years with a 4% interest rate compounded monthly.