Before any explanation, a simulation: put R$ 368 mil on Renda+2035 now, with the interest on that title around 6.40%, and don't do anything else
This will guarantee R$5,000 today per month over 20 years, between 2035 and 2054 – all religiously adjusted for inflation.
If you can wait longer than that, the better. Anyone who is 35 years old today and wants to start receiving payments around 65, when they retire, can invest in a longer title: Renda+2055. In this case, a deposit of R$ 105 mil now to guarantee the same R$5,000 for 240 months; from 66 to 86 years old.
Note that R$5,000 for 240 months gives a total of R$1.2 million. And you only invested R$105 thousand. We are talking about an accumulated income of 1.042% – real income, above inflation (more details later). In the other case, that of extra retirement from 2030, the return is less stratospheric: 226%.
Remember that movie with Justin Timberlake, the The Price of Tomorrowfrom 2011? The currency there is lifespan. A cup of coffee costs a few seconds; a car; a good few years. The rich have assets spanning centuries, millennia; therefore, they live as long as they want (in the film's mythology, science discovered how to make people immortal; but the government determined that money is time, so only ultra-high-income people live forever) – below, the character from Justin “do a Pix”, transferring life expectancy:
This film has aged well because real life is similar. Time is money, yes – and in a much more literal way than the phrase suggests. Courtesy of compound interest. If you are 25, for example, you can go for the longest of all Renda+, the 2065 and enjoy a flood of them.
In fact: a contribution of withered R$ 56 mil At this point it would be enough to earn R$5,000 per month over 20 years – between 2065 and 2084. Total profit: 2.043%.
Once the simulation is done, let’s get to the explanation.
The mechanics of IPCA+
Renda+ public bonds emerged recently, in 2023, and bring a truly unique degree of predictability for those who want a complementary retirement. Because only with it can you know exactly how much you will earn per month in the future – in today's moneyadjusted for inflation.
Renda+ is a derivative of public bonds of the IPCA+ type. It is worth noting that “IPCA+” is the fancy name that the Treasury gave to the thing; the technical name for this type of title is different: NTN-B.
A bond is a debt. A public bond, a debt that the government owes you. An NTN-B is a paper that the government sells to you through Tesouro Direto. A virtual piece of paper that, if it were a real piece of paper, would read: “This is worth R$ 4,330 in the future, corrected by the IPCA; payment date: May 15, 2035. Signed: National Treasury”.
“Adjusted by IPCA” means that in 2035 you will receive an amount that guarantee purchasing power which R$4,330 they have today. If inflation stays at an average of 4% per year from now until then, the nominal value of this will be R$6,600. If it stays at 7%, R$9.1 thousand. But face value is useless. It's just an empty number. The value real of the amount will be R$4,330 today – regardless of what inflation happens between now and maturity.
And how much would you pay for this paper that the government sells? If it were R$4,330, the thing would only yield inflation. It's not worth it. Even savings pay more than inflation.
In the real world, on October 9, 2024, the NTN-B maturing in 2035 was worth R$ 2.259 (for those who wanted to buy on the Tesouro Direto website). The difference between R$2,259 and the R$4,330 we mentioned are the real interest that NTN-B pays. In this case, the equivalent of 6.38% per year.
The R$4,330, it is worth noting, are what the Treasury calls the “updated nominal value”. The VNA. It rises a little every day to compensate for inflation. This guarantees correction by the IPCA. That's why the fancy name for NTN-Bs is “IPCA+” – it pays inflation more the interest.
Renda+, our subject here, is also an NTN-B. But a somewhat unusual NTN-B. Each Renda+ title is made up of 240 NTNBs – precisely because it was designed to be a private pension tool. An extra pension. This is what we will understand better now.
How Renda+ works
Enter the Tesouro Direto website and you will see several Renda+ titles, each with a date in front (Renda+2030; Renda+2035…). In IPCA+ bonds, this date marks the maturity of the bond. In Renda+, no.
This is the “conversion date”. The date on which you start receiving your extra pension.
This extra retirement will last 240 months (20 years) precisely because each Renda+ bond is made up of 240 separate NTNBs, each with a maturity date – the day on which the government pays, and the money enters your account. To visualize it better, let's take a specific Renda+ security, the 2035.
To make the math extremely easy, let's imagine that you bought 240 titles, at R$1,300 each. In this case, it is as if each of these expires in a specific month. The first, in January 2035, the second in February… until the last; which will fall in December 2054.
How much will fall per month? The VNA; in other words, those R$ 4,330 in today's money that we have talked about so much here.
Do you want to receive R$5 thousand? Ok. Instead of buying 240 titles, put 277,13 of them in the cart – you can buy fractions of titles too.
To make visualization even easier, let's imagine a reality absurd: that inflation will be zero between now and January 2035. In this crazy scenario, with 277.13 bonds in hand, the nominal value you would receive would be exactly R$5,000. But then, precisely in January 2035, inflation decides to return. The IPCA for that month is 1%.
Quiet. The February installment of your retirement also increases by 1%. It goes for R$5,050. That's it: the installments are protected from inflation.
Price formation
Renda+’s math is extremely ingenious. One of its creators is Nobel laureate Robert Merton, and Brazil was the first country to create a public title with this formula.
Roughly speaking, it works like this: whatever the built-in interest rate, NTN-Bs maturing in 2054 accumulate MUCH more compound interest than those maturing in 2035. This means that NTN-Bs 2054 should be much cheaper to buy. who acquires today than the NTNB-s 2035.
And that's exactly what happens. Those due in 2035, with interest rates of around 6.40%, should cost R$2,200. At 2054, well less than R$1 thousand. The Income+ formula, then, does the following: take an average. This way, the cake of 240 NTN-Bs is sold in a package at an intermediate price. In this case, R$1,300. And for every R$1,300 deposited right now, you will receive R$4,300 later on – the 226% we talked about at the beginning.
This surrealistic performance is not even an intrinsic characteristic of Renda+. It only happens because interest rates today are at a historically high level – throughout history, the NTN-Bs that have been circulating for the longest time only paid interest above 6% on 26% of trading days.
Getting a higher interest rate means buying the paper at a relatively low price. This is the opportunity that exists today. It exists because Selic is high. The current 10.75% is equivalent to IPCA+6.33%. That's why NTNBs are paying in this range.
But if everything goes well (read “fiscal part”) the Selic will fall in the coming years. The chance that exists now, then, is to lock in interest rates outside the curve for decades. In other words: using a storm in the economy, which demands exorbitant interest rates, to guarantee a greater bonanza in retirement.
Like everything in life, there is a risk: that the Selic will continue to rise and remain on a high plateau into the 21st century. If this happens, you lose due to the opportunity cost. The interest rates on future NTN-Bs could become even higher. The price of bonds will then be even lower. And you will find that you could have paid a lot less. An unlikely scenario, but not impossible.
Because tomorrow always has a price. But, in the world of finance, you can only know if the price was worth it when tomorrow actually arrives.
to understand Renda+ taxation, among other details, see here.
To find out more about the current moment of interest rates, see here.
To check how far you are the Updated Nominal Value of NTN-Bs, see here.