Final answer:
To calculate the future value of $3,000 at a 4% interest rate compounded quarterly over six months, use the formula FV = P (1 + r/n)^(nt). This results in an approximate value of $3,060.30.
Step-by-step explanation:
The subject is asking how much a principal amount of $3,000 would earn in six months at an interest rate of 4%, compounded quarterly. To calculate the future value in this case, we can use the compound interest formula:
FV = P (1 + r/n)nt
Where
P is the principal amount ($3,000)
r is the annual interest rate (4% or 0.04)
n is the number of times the interest is compounded per year (quarterly means 4 times a year)
t is the time the money is invested for, in years (in this case, 0.5 years since we're calculating for 6 months)
Now let’s substitute these values into the formula:
FV = $3,000 (1 + 0.04/4)4*(0.5)
Calculating the parenthesis first:
(1 + 0.04/4) = 1 + 0.01
= 1.01
Now we raise this to the power of 2 (since 4 quarters * 0.5 years):
1.012 = 1.0201
Finally, we multiply this by the principal amount:
FV = $3,000 * 1.0201
= $3,060.30
So after six months, the $3,000 invested at an annual interest rate of 4%, compounded quarterly, will have grown to approximately $3,060.30.