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Math · Consumer Math

Chapter 3: Saving and Interest

Savings Accounts and Rates

Reading the rate that is actually offered.

Lesson
2
Time
About 21 minutes
0 of 12 done

Step 1: Let's Learn

Read it, or press Listen and follow the words.

The annual percentage yield states what an account actually earns in a year, with compounding already included.

Why it exists

A 5% rate compounded monthly beats 5% compounded annually. APY puts both on one comparable number.

Frequency has limits

More frequent compounding helps, but the gain shrinks quickly. Daily is barely better than monthly.

Inflation

Inflation reduces what money buys. An account paying 2% while prices rise 3% loses purchasing power.

Real return

The real return is roughly the rate minus inflation. That is the number that matters.

Access has a price

Accounts paying more usually restrict withdrawals. Emergency money belongs in the accessible account, even at a lower rate.

Nominal rate against effective rate

The advertised annual rate ignores compounding; the effective annual yield includes it. Comparing accounts requires the effective figure, which is why it is the one legally required to be disclosed.

Real return subtracts inflation

An account paying 2% while prices rise 3% loses purchasing power. The nominal return is positive and the real return is negative. Any comparison of savings over time has to account for this.

Fees reduce the rate

Monthly maintenance charges, minimum balance penalties and transaction fees all subtract from the return. An account with a headline rate and a monthly fee can pay less than one with a lower rate and none.

Access and rate trade off

Accounts paying more usually restrict withdrawals or require notice. Matching the account to when the money will be needed is the decision; a higher rate on money you cannot reach when required is not an improvement.

Step 2: Try It Yourself

Tap and try it out.

Three accounts. Compare the yields, then subtract inflation to see what each really returns.
Account A20
Account B41
Account C50

Account C has the most. It has 30 more than Account A.

Step 3: Watch an Example

One step at a time.

Watch Marcus Find the Real Return

Marcus has an account paying 2% APY while inflation runs at 3%.

  1. Step 1

    The balance genuinely grows: $1000 becomes $1020 after a year.

Step 4: Your Turn

Practice makes it stick.

The Real Rate

Problem 1 of 2

An account pays 5% while inflation is 2%. What is the approximate real return, in percent?

%

The Loss

Problem 2 of 2

An account pays 1% while inflation is 4%. Approximate real return, in percent?

%

Compare the Accounts

1 of 8

Pays 6%, inflation 2%. Real return in percent?

2 of 8

Pays 3%, inflation 3%. Real return in percent?

3 of 8

$1000 at 2% APY for one year. Balance in dollars?

4 of 8

$5000 at 4% APY for one year. Balance in dollars?

5 of 8

Which is better, all else equal? 1 for 5% APY, 2 for 4.1% APY.

6 of 8

Where should emergency money sit? 1 accessible account, 2 locked higher-rate account.

7 of 8

Which statements about APY are true?

8 of 8

Pays 2%, inflation 5%. Real return in percent?

Step 5: Quick Check

Show what you know.

Question 1 of 2

An account pays 4% while inflation is 1%. Real return in percent?

Question 2 of 2

What does APY let you do?

What You Learned

  • APY states the true annual earnings, with compounding included.
  • The real return is roughly the rate minus inflation.
  • Emergency money belongs where it can be reached, even at a lower rate.