Question

If $300 is invested at a rate of 6% per year and is compounded quarterly, how much will the investment be worth in 12 years?

$145.23
$358.69
$613.04
$618.41

Answer 1

Answer:

$613.04

Step-by-step explanation:

Compound Interest Formula:

   $A = P(1+\frac{r}{n})^{nt}$

   n = number of compounds

   t = time

   r = interest rate

   P = principle amount (original amount)

   A = final amount

Since it's compounded quarterly, that means there will be 4 compounds per year, so n=4. The interest rate has to be converted to the decimal value, and this is done by simply dividing it by 100 to get r=0.06.

Plug Values into equation:

$A = 300(1+\frac{0.06}{4})^{12*4}$

Simplify inside parenthesis

$A = 300(1.015)^{48}$

Calculate exponent

$A \approx 300(2.043478)$

Multiply values

$A \approx 613.04348$

Round

$A = 613.04$