How much money should be deposited today in an account that earns 6% compounded semiannually so that it will accumulate to $14,000 in three years?

The amount of money to be deposited today is $11,725

Step-by-step 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