Financial Math
How much should be invested at 8% compounded semiannually in order to have $5000 at the end of 8 years?
Hello, steph!
You're expected to know the compound interest formula:
. . $\displaystyle A \;= \;P(1 + i)^m$
. . where: .$\displaystyle \begin{array}{cccc} a\:= \\ P\:= \\ i\:=\\n\:=\end{array}
\begin{array}{cccc}\text{final amount} \\ \text{principal invested} \\ \text{periodic interest rate} \\ \text{number of periods}\end{array}$
How much should be invested at 8% compounded semiannually
in order to have $5000 at the end of 8 years?
We are given: .$\displaystyle \begin{array}{ccc}A\:= \\ i\:= \\ n\:=\end{array}
\begin{array}{ccc}5000 \\ 8\%/2 = 0.04 \\ 2\times8 = 16\end{array}$
So we have: .$\displaystyle 5000 \;=\;P(1+0.02)^{16}$
Then: .$\displaystyle P \;= \;\frac{5000}{(1.02)^{16}} \;=\; 3642.229069$
Therefore, $\displaystyle \$3,642.23$ should be invested.