If $800 is invested for x years at an annual rate of 9%, compounded quarterly, the future value that will result is
Determine the value of the investment after 5 years. Round your answer to two decimal places, if necessary.

A)$2,241.76
B)$4,483.53
C)$1,230.90
D)$3,683.53
E)$360

Question

If $800 is invested for x years at an annual rate of 9%, compounded quarterly, the future value that will result is ​  ​
Determine the value of the investment after 5 years. Round your answer to two decimal places, if necessary.
​
A)$2,241.76 
B)$4,483.53 
C)$1,230.90 
D)$3,683.53 
E)$360

Quizplus · Accepted Answer

The formula for compound interest with quarterly compounding is:
$$A=P\left(1+\frac{r}{n}ight)^{nt}$$
where:
$A=$ the future amount (what we're trying to find)
$P=$ the principal amount (initial investment)
$r=$ the annual interest rate (as a decimal)
$n=$ the number of times the interest is compounded per year
$t=$ the time (in years)

Plugging in the values given in the problem, we get:
$$A=800\left(1+\frac{0.09}{4}ight)^{(4)(x)}$$
Simplifying the inside of the parentheses gives:
$$A=800\left(1.0225ight)^{(4)(x)}$$
Since we want to find the value of the investment after 5 years, we can substitute $x=5$:
$$A=800\left(1.0225ight)^{(4)(5)}=800(1.0225)^{20}=4,483.53$$
Rounding to two decimal places, we get $A=\boxed{	ext{(B) }4,483.53}$.

If $800 Is Invested for X Years at an Annual