The basic idea of retirement is that we work for a while, and then we retire either because we can’t or don’t want to work anymore. For this to be possible, you need to save for retirement while you work.

The government incentivizes this saving by providing each person special accounts that have tax advantages. These accounts have fancy names like individual retirement account (IRA) or defined-contribution retirement account (401k), but to keep things simple let’s just call them retirement accounts.

The alternative to retirement accounts is a taxable account (e.g., Robinhood is a taxable account). We call these “taxable” accounts because you pay more taxes on money in these accounts.

Retirement accounts have two key advantages over taxable accounts:

**Key Advantage 1 - No capital gains tax:**For example, when you invest $1,000, and it turns into $5,000 in a taxable account, you have to pay something like 15% on the gains in taxes, which is ($5,000 - $1,000) * 15% = $560. In a retirement account, you get to keep all $5000.**Key Advantage 2 - No taxes on dividends:**Most stocks pay out some of their returns in dividends each year. In a taxable account, you have to pay income tax on this dividend every year. In a retirement account, you keep the entire dividend. Dividends are usually relatively small, so this seems like a small difference, but it happens every year, so the difference compounds and can become gigantic over time.

Conventional wisdom is that everyone should use a retirement account, but many people don’t. **38%** of Americans don’t have a retirement account, and its worse for younger, lower-income, and minority individuals.

How bad is it not to have a retirement account? Is it like you should eat three cups of vegetables each day, but if you don’t, you’ll in all likelihood be fine? Or are the consequences of not having a retirement account more dire? How much money are individuals not using a retirement account missing out on? How much worse off will they be in retirement?

Let’s try to answer these questions to make the value of retirement accounts concrete. Imagine you have $1000, and you’re trying to decide what to do with that money. For simplicity, further, imagine that the only thing you care about is buying shoes that cost $100 a pair. You plan to retire in 35 years and have three distinct options:

**Option 1 - Buy shoes now:**You can buy $1000 / $100 = 10 pairs of shoes right now.**Option 2 - Invest in a taxable account for 35 years:**You invest your $1,000 in a taxable (non-retirement) account. After paying income tax on dividends each year and capital gains at the end, it turns into $4,392. You can then buy $4,392 / $100 = 43.9 pairs of shoes in retirement.**Option 3 - Invest in a retirement account for 35 years:**You invest your $1000 in a retirement account. You don’t have to pay taxes on dividends or capital gains, so it turns into $5,516. You can then buy $5,516 / $100 = 55.2 pairs of shoes in retirement.

We can think of the differences between these options in terms of multipliers. The multiplier between Option 1 and Option 2 is 43.9 / 10 = 4.39. You can have more than four times more pairs of shoes if you’re willing to wait for retirement. Let’s call this the investment multiplier:

$$ \small{\text{Investment Multiplier} = \dfrac{\text{Purchasing power of \$1 if invested in a taxable account}}{\text{Purchasing power of \$1 right now}}} $$

The investment multiplier is how much more purchasing power you’ll have if you invest your money into a taxable account. It clarifies the tradeoff between consuming now and consuming in retirement: Would you rather have one pair of shoes now or four pairs of shoes in retirement? This is the tradeoff between consuming less now or more later: The classic marshmallow test on a longer time scale.

The investment and retirement multipliers depend on four factors:

- Time invested (the example above assumes 35 years)
- Growth rate (3% real)
- Dividend rate (2% real
^{1}) - Capital gains rate (15%)

The multiplier between Option 2 and Option 3 is 55.2 / 43.9 = 1.26. Given that you’re planning to wait 35 years to buy shoes, you can have 1.26 times more pairs of shoes if you invest in a retirement account. Let’s call this the retirement multiplier:

$$ \small{\text{Retirement Multiplier} = \dfrac{\text{Purchasing power of \$1 if invested in retirement account}}{\text{Purchasing power of \$1 if invested in a taxable account}}} $$

The retirement multiplier is a free increase in the number of shoes you get. In either case, you’re waiting until retirement to buy shoes, but simply by using a retirement account and getting the two key advantages, you get more shoes. You’d be silly not to! I’m working on a Retirement Multiplier calculator.

If you want to know how your purchasing power will increase if you invest in a taxable account, simply multiply by your Investment Multiplier (4.39 in the example). If you want to know your purchasing power will increase if you invest in a retirement account, multiply by your Investment Multiplier and Retirement Multiplier (4.39 x 1.26 = 5.52 in the example).

- Assuming real returns of 2% dividend and 3% growth each year totals a 5% annual real return. Working in real returns avoids having to worry about correcting for inflation.
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