Question

How much would $300 invested at 4 percent interest compounded monthly be worth after 8 years round your answer to the nearest centA. $410.57B. $412.92C. $484.25D. $308.10?

Answer 1

We will use the equation  $A(t)=P(1+ \frac{r}{n})^{(n)(t)}$, where P is the initial amount invested, r is the interest rate in decimal form, n is the number of times in a year the money is compounded, and t is the number of years the money will be invested.  Our P = 300, r = .04, n = 12 (there are 12 months in a year), and t = 8.  Filling in accordingly,  $A(t)=300(1+ \frac{.04}{12})^{(12)(8)}$.  Simplifying what we can gives us  $A(t)=300(1+.00333333)^{96}$.  Doing that addition inside the parenthesis and then raising that number to the 96th power gives us A(t) = 300(1.376395075)  so A(t) = $412.92, choice B above.