Question

2. An investment company pays 9% compounded semiannually. You want to have $8,000 in the future. How much should you deposit now to have that money 5 years from now?

Answer 1

Answer:

$5151.42

Step-by-step explanation:

The formula you need is

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

where A(t) is the amount after the compounding, P is the initial investment, r is the interest rate in decimal form, n is the number of compoundings per year, and t is time in years.  The info we have is

A(t) = 8000

P = ?

r = .09

t = 5

Filling in we have

$8000=P(1+\frac{.09}{2})^{(2)(5)}$

Simplifying a bit and we have$8000=P(1+.045)^{10}$

Now we will add inside the parenthesis and raise 1.045 to the 10th power to get

8000 = P(1.552969422)

Divide away the 155... on both sides to solve for P.

P = $5151.42