First we need to figure out how much John would have made had he invested in option number 1.

So we use the compound interest Formula A = P (1+r/n)^{nt}

A = final amount

P = Initial Balance

r = interest rate

n = number of times interest rate is applied per time period

t = number of time periods elapsed

So P = 10,000; r = 0.08 (8%); n = 1; t = 6 because the interest is annual and only occurs once a year

10,000(1+ 0.08/1)^{6} = $15,869

Ok so we know **he would have had $15,869 had he invested in the first option.**

We need to know how much he has left now.

He initially had 100 shares of $100 each but they lowered in value to $90 each after a year. He sold all 100 for $90 each which means he had $9000 left.

So now we need to use the formula again to figure out the annual rate that he would need to reach $15,869 in 5 years.

The easiest way is to **work backwards.** Enter each value r into the equation and solve for A.

Lets try 12%

A = 9000 (1+ 0.12/1)^{5}

A = 15,861

Lets try 12.5%

A = 9000 (1 + 0.125/1)^{5}

A = 16,218

We know 11% will be too low and 13% will be too high.

The question is a little finicky in asking "approximately...what annual rate...would be equal to the first option".

$15,861 is approximately right but is not *quite *equal to $15,869 but I believe that is the answer.

**ANSWER 12%**

If you have any questions please let me know!

Samantha W.

07/20/21

Thiago W.

Thank you so so much!07/20/21