Answer:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount of money accumulated, P is the principal (initial) amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this problem, we want to find the principal amount P that will accumulate to $12,000 in 3 years at an annual interest rate of 6% compounded monthly. First, we need to convert the annual interest rate to a monthly rate:
r = 0.06/12 = 0.005
Next, we can substitute the given values into the formula and solve for P:
12,000 = P(1 + 0.005/12)^(12*3)
12,000 = P(1.005)^36
P = 12,000/(1.005)^36
P ≈ $9,883.86
Therefore, the amount of money that should be deposited today is approximately $9,883.86.
Explanation: