# Don't Have A Clue!!

• Nov 28th 2006, 04:28 PM
steph
Don't Have A Clue!!
Financial Math

How much should be invested at 8% compounded semiannually in order to have $5000 at the end of 8 years? • Nov 28th 2006, 05:10 PM Soroban Hello, steph! You're expected to know the compound interest formula: . .$\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}$Quote: 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.