I've been trying to figure out when it is correct to use Imasu instead of Desu.

Ex 1 ...Anata wa toshi wo totte imasu. - You are old
Ex 2 ...Anata wa wakai desu. - You are young

Please explain to me why example 1 is "imasu" and not "desu".

My computer doesn't recognize Hiragana or Katagana, so please use Romaji. Thanks for any help with this one

In your examples you are using the desu with an adjective and the imasu with a verb.

In other examples imasu is used for people and animals to say "they are" and arimasu is used for inanimate things.

Get a good Japanese grammar book and study up

Here's a word of advice: Start using kanji/kana and stop relying on romaji. When people get lazy and don't want to move past alphabets, it causes all sorts of weird mixups that are unnecessary and a pain to correct. Keeping this in mind, let's go back to your question.

Any time you want to say X is Y, the grammatical structure you use is X wa Y desu. Desu by itself doesn't have a meaning, but when you have a subject and the sentence ends in desu, you can think of it as an equal sign. [Subject] = [Whatever is after it]. Likewise, your sentence "Anata wa wakai desu" can be interpreted as You = Young. In other words, "You are young".

Now let's move on...

In your other example, you want to say someone is old. However, you should know that "X wa toshi o totteimasu" is pretty much a set phrase. It's a roundabout way of saying someone is old because there isn't really a verb for an "old" (person). Instead, Japanese people like to say that a person has "taken a lot of age" to express that same idea. It's used quite often, but there's a lot of grammar behind it. Let's break it down a bit.

Imasu is the polite form of iru, which means to exist (For animate objects only). As you can see, "X is Y" is quite different from "X exists". However, "Toshi o totteimasu" goes several grammatical step further. It uses the Verb + te-imasu form. This grammatical structure expresses (in most cases) any of the following:

1) A continuing action
2) A repeated action
3) A resulting state of an action

When someone has quite literally "taken age", it's most appropriate to conjugate the verb toru into totteimasu because it expresses all 3 of the ideas listed above. When you age, it's continuous and repetitive. Also, when you are old, it is the resulting state of aging.

So in a nutshell, desu and imasu is basically comparing apples with oranges. To make things even more confusing, you used examples that went like 10 gramatical steps beyond what you are currently trying to learn. Had you stuck with kanji/kana from the start, you would've visually seen the complex grammar structure and picked up on some of it before the question even came to mind.

Hopefully, that answers your question.