Part $2$: Investments $(15$ points$)$

Another component of financial security is planning for retirement; one of the ways you can save is mutual funds, otherwise known as $401$K retirement accounts. Below is a snapshot of two mutual funds. I want you to compute the interest rate on each investment over time period $2003-2020$ that this information represents.

So$,$ here are the principle $($P$)$ or initial investments for each:

American Balanced Fund $-$ $$12,000\mathrm{.}00$ The Growth Fund of America$-$ $$12,000\mathrm{.}00$

Here are what each investment is currently worth $($FV$)$:

American Balanced Fund $-$ $$37,600$ The Growth Fund of America $-$ $$40,500$

To compute the average rate for both investments $$i$,$ use the formula from $5\mathrm{.}2,$ where you are compounding monthly: FV$=$P$(1+$i$)^$n$.$ Don$$t forget to convert $$i$$ to an APR.

Complete the table showing all work.

American Balanced Fund The Growth Fund of America

Compute how long will it take for the su m of the two investments $($$$78,100)$ to reach $$500,000$ using the average of the two rates $7\%?$ Use yearly compound formula and solve for n:

FV$=$P$(1+$i$)^$n$.$