Question

57miScore: 2173/7 answeredQuestion 3

Answer 1

Step-by-step explanation

Given

`\begin{gathered} Amount=$ \text{ \$}500,000 $ \\ Time=30years \\ rate=4\text{\%} \\ principal=? \\ n=12 \end{gathered}`

We can use the formula below to find how much would you need to deposit now into the account to reach your retirement goal.

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \end{gathered}`

Therefore;

`\begin{gathered} 500000=P(1+((4)/(100)/12))^(12*30) \\ 500000=P(1+((4)/(100*12)))^(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\}} \\ (P\cdot\:1.0033333^(360))/(1.0033333^(360))=(500000)/(1.0033333^(360)) \\ P=150899.7373 \end{gathered}`

Answer:

`\begin{equation*} 150899.7373 \end{equation*}`