How does inflation affect the value of savings?

Well, I got basically a question about economics of our world, I hope I'm wrong in my assumptions, because it's pretty ugly and I'm really hope it's more about me being wrong than it's actually the truth. So...:

What does inflation actually means when we talk about savings? For example, If Joe works his ass off and makes some savings in US dollars and puts them in the bank. So say Joe's savings are about \$100,000 and he decides to transfer them to his kid's bank account so when his kid grows up his kid could take the money. But, as I understand it, this \$100,000 won't be the same \$100,000 in about 20 years, when Joe's kid has grown up and wants to take the money. Instead he would get much less than \$100,000, because each year the inflation will eat out by at least 1.5% (avg. for my opinion for Western countries) of this money. Is this really how it is?

If Joe put \$100,000 in a mattress or in a bank account that pays a 0% rate, then yes, in 20 years if inflation has risen by 1.5% annually, then the money will only be worth about \$74,000 in today's dollars. But if he saves the money in an account that pays a higher interest rate than inflation (or buys a financial instrument like TIPS, a type of government bond that pays an inflation-adjusted return), his kids will have an amount of money equal to more than \$100,000 in today's dollars. The yield to maturity on a TIPS bond maturing in 2040 is currently about 0.9%, which isn't very high, but that's a nearly risk-free investment that is protected against inflation. If Joe bought one of these, his kids would have about \$100,900 in today's dollars. If he instead took on a certain amount of risk, his kids could have potentially much more.