Answer:
The amount of money to be deposited today is $11,725
Explanation:
In this question , we are concerned with calculating the amount of money that should be deposited presently to have $14,000 in three years.
To get this, we have to use the compound interest formula
A = P( 1+ r/n)^nt
where A is the amount to be earned after the end of the compounding period which is $14,000 according to this question
P is the initial amount to be deposited which is what we are looking for
r is the rate of compounding which is 6% or simply 6/100 = 0.06
n is the number of times interest is compounded yearly which is semiannually according to the question and this means 2
t is the number of years which is 3 according to the question
Now, plugging all these values, we have;
14,000 = P( 1 + 0.06/2)^(3 * 2)
14,000 = P(1+0.03)^6
14,000 = P(1.03)^6
14,000 = 1.194P
P = 14,000/1.194
P = 11,724.77 which is approximately $11,725