Question

Which of these expressions represents how much money you will have at the end of one year if interest is compounded semiannually at 6% on a $3,000 deposit?

Answer 1

Using compound interest, it is found that you will have $3,182.7.

Compound interest:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

• A(t) is the amount of money after t years.  

• P is the principal(the initial sum of money).  

• r is the interest rate(as a decimal value).  

• n is the number of times that interest is compounded per year.  

• t is the time in years for which the money is invested or borrowed.

In this problem:

• Compounded semiannually, hence $n = 2$.

• 6% interest, hence $r = 0.06$.

• Deposit of $3,000, hence $P = 3000$.

• End of one year, hence $t = 1$.

Then:

$A(1) = 3000\left(1 + \frac{0.06}{2}\right)^{2} = 3182.7$

You will have $3,182.7.

To learn more about compound interest, you can take a look at brainly.com/question/25781328