Explanation
Given
[tex]\begin{gathered} Amount=$ \text{ \$}500,000 $ \\ Time=30years \\ rate=4\text{\%} \\ principal=? \\ n=12 \end{gathered}[/tex]
We can use the formula below to find how much would you need to deposit now into the account to reach your retirement goal.
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \end{gathered}[/tex]
Therefore;
[tex]\begin{gathered} 500000=P(1+(\frac{4}{100}\div12))^{12\times30} \\ 500000=P(1+(\frac{4}{100\times12}))^{360} \\ 500000=P(1+0.0033333)^{360} \\ 500000=P(1.0033333)^{360} \\ Switch\:sides \\ P\left(1.0033333\right)^{360}=500000 \\ Divude\text{ both sides by }1.0033333^{\left\{360\right\}} \\ \frac{P\cdot\:1.0033333^{360}}{1.0033333^{360}}=\frac{500000}{1.0033333^{360}} \\ P=150899.7373 \end{gathered}[/tex]
Answer:
[tex]\begin{equation*} 150899.7373 \end{equation*}[/tex]
