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Discussion
Taylor is 25 years old and opens a workplace retirement plan. She decides to put away some money into it every month until she turns 65, the age she will retire. The account earns about 7% interest annually.
The retirement plan will pay her a fixed amount every month after her retirement until her 95th birthday.
Why should Taylor do this instead of just keeping her cash in a checking account?
How can a pile of money pay a ‘salary’ for 30 years without running dry?
Part (a)
A regular checking account pays almost no interest (often well below 1% per year), so any money you leave there barely grows and in fact loses value due to inflation.
In contrast, Taylor’s retirement plan grows at about 7% each year, so her contributions add up and compound over 40 years to create a much larger fund.
Keeping cash in her checking account would leave her with considerably less at age 65 that she would be able to withdraw over the next few decades.
Part (b)
The reason a lump sum can “pay” a fixed monthly amount for 30 years without ever running dry is exactly the reverse of how it was built up: the money stays invested to grow at 7% annually, so even as you withdraw a “salary,” the remaining balance continues to earn interest.
In the compounding section, we learned how each contribution earns interest on itself over time, causing the value of the account to “snowball.”
In retirement, that same snowball effect works in reverse:
Each month of retirement, the fund first earns interest on whatever is left.
You then withdraw your “salary.”
The interest portion of the withdrawal is simply the fund’s earnings, and the rest comes out of the pile itself.
Because the retirement plan sets the monthly paycheck to exactly the right size, each month’s interest helps cover part of that check, and only the rest comes out of the savings pile.
The "pile" shrinks slowly and predictably—just enough each month—so that after the last of the checks is written, the balance is exactly zero. No money is left on the table, and the fund never runs out early.
Taylor's retirement account (once she has retired) is an example of an annuity.
An annuity is a type of account that a person can live off when they retire. They make regular withdrawals, and the interest on the account allows the money to last longer. The money in an annuity account is often built up over a lifetime of saving and compounding, but it can also be deposited in a lump-sum.
Effectively, an annuity is the reverse of a loan. Instead of the bank lending you money, you lend the bank money, and they make regular repayments back to you over time.
Take a look at the graphic below to see what a full financial future might look like: with consistent saving, retirement, and an annuity account that pays out until some set age.
Powered by Desmos
Discussion
What do you notice from the interactive above? Do you see any benefits that might arise from an annuity account? How might this influence your financial plans in the future?
The interactive shows that your balance doesn’t grow by the same amount each year—it accelerates over time. This creates a J-shaped curve rather than a straight line, reflecting what we learned about the power of compound interest: you're not just earning interest on your original savings, but also on the interest those savings have already earned.
Even small increases in your interest rate—or just a few extra years of saving—can dramatically boost your final balance.
Annuities are especially valuable because they can turn a lifetime of regular contributions into a reliable stream of future income, powered by the effects of compound interest over time.
Some other key observations:
Starting early gives your money more time to grow exponentially.
Higher interest rates (or more frequent compounding) amplify long-term gains.
Regular contributions quickly snowball, since every payment begins generating interest of its own.
That’s why, when planning for the future, it’s smart to begin saving or investing as soon as possible, prioritize accounts with strong compound-interest potential, and contribute consistently.
The earlier you start, the more powerful the growth.
In the graphic above, the annuity account comes into play upon retirement. This is when we start making regular withdrawals until some set age.
As the account balance gets smaller, it earns less interest—just like a loan gathers less interest as you pay it down. Despite this, just like with loan payments, the bank's payments to you remain fixed the whole time.
Using TVM Solver (Calculator) - Annuities
You should be able to use the TVM Solver on your calculator to perform calculations with annuities.
In IB, annuities are paid at the end of a number of periods (N) and have an annual interest rate (I%), an initial lump-sum deposit (PV), a fixed payment (PMT) and a future value (FV), which represents the total accumulated amount at the end of the term.
In the special case of annuities, payments and compounding occur can occur at different same frequencies (P/Y & C/Y).
Exercise
Madeline retires at age 65 with $1,000,000 in her savings fund, which she immediately rolls over into an annuity fund that earns 3% p.a. interest compounded semi-annually.
How many payment periods will Madeline's money last for if she withdraws $10,000 monthly?
Select the correct option
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Positive & Negative Cash Flows (TVM)
Whenever you use the Finance App (TVM Solver) on your calculator, it's critical that you enter and interpret the signs correctly:
When you receive money from a bank or savings account, that value is positive, because you're gaining money.
When you send money to a bank, that value is negative, because you're losing money.
In the context of annuities:
The person deposits a lump-sum with the bank, which is a cash outflow, so PV is negative.
The person receives regular repayments, which is a cash inflow, so PMT is positive.
Additionally, annuities are the special case where P/Y and C/Y may differ:
If the account compounds annually, but pays out monthly, P/Y=12 but C/Y=1.
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