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I've heard anecdotes about high-interest savings accounts (4.5% around 2006, even 8% in the 80s), that were opened when interest rates (federal funds rate) were high. The implication seemed to be that for some of these accounts, if one were to hold these accounts open, they'd still be getting the same rates after all these years. Do I misunderstand, or is this actually possible?

Flexible savings accounts are almost all variable interest, meaning the rates go up and down with market rates. The reason for this is that if they did not, people could pay into the fixed interest ones when rates elsewhere were low, and take money out when rates elsewhere were high (and invest it at a higher rate in other accounts), making a profit at the bank's expense.

There is a vehicle for 'locking in' savings at high interest rates. This is an account where the interest rate is fixed, but the money is also locked into it. In America these are called Certificate of Deposit (CD). In Canada they are called Guaranteed Investment Certificates (GIC). In the UK and other places they are called Term Deposits. In essence you agree to lock your money into an account for a fixed amount of time, in return for a guaranteed rate of return. (There is usually a clause that allows you to take your money out early, often with a penalty.)

I've heard anecdotes about high-interest savings accounts (4.5% around 2006, even 8% in the 80s).

Well, you heard wrong (g). In 1980-81 the Fed Funds rate peaked at 17.36%. Taxable money market funds were paying over 17%. Short term CDs were over 18%. The 10 and 30 year treasury bonds were over 15%. Baa corporate bonds were paying over 16%. Long term treasury and corporate bonds locked in these rates.

I was fairly new to the market then. A market mentor of mine had recently retired and had sold his business for $600k. He put the bulk of it in 20-30 paper and happily cut coupons at an average rate of 15% until maturity. Think about that. 15% on say $500k is a tidy income of $75k per year. Not bad at all.

There is an element of truth to this, but not in savings accounts. When I was very young, some family members bought a small amount of Savings Bonds issued by the U.S. government which at the time were offering in the vicinity of 9% interest. Twenty years later they were cashed in to help pay for my college education - a shame really considering they would have continued paying this for another (IIRC) twenty years, but in the grand scheme of things it wasn't a huge amount of missed opportunity, as the cashed in amount was somewhere around two to three thousand dollars.

There are similar investment strategies you could pursue. They all revolve around the idea of locking in an interest rate in long term debt obligations with a debtor with very low risk of default. The U.S. Savings Bonds example is an outlier because they pay interest for a much longer period of time and don't "mature" in quite the same way as typical bond issues do.

That depends on the contracts you have and probably also in the country, related with available products.

In Germany, we have "Bausparverträge" (building saving contracts) where we pay a certain amount per year to save up some money. After reaching a certain threshold, we qualify for a loan at an interest rate defined on signing the contract (but are not required to take the loan).

When you signed such a contract in a period of high interest, you have this high interest even nowadays. For examples, my two contracts from 2007 and 2013 both still come with an interest of 3%, without risk of the market. Compared to that, normal saving accounts offer in the range from 0.01% to about 0.5% (or 0.9% if you are lucky).

The downside is that if I urgently need the money, the contract and its benefits are gone.

Long story short, yes, it is possible to lock in a high interest rate if you choose the right product.

Savings accounts generally aren't for fixed amounts. There have, however, been special promotional offers for accounts with fixed interest rates. I think that has become rarer, and certainly finding one with an interest rate of 4.5% would be unlikely to say the least.