Saving and investing: interest, compounding, risk and return

Grade 12 Social Studies Worksheet

Circle the best answer.

1. Read this first

   The federal funds rate and the CPI, 2021 to 2024 (Federal Reserve Board and BLS, read Nov 14, 2026)

   Year	Average federal funds rate (percent)	CPI-U yearly average (1982-84 = 100)
   2021	0.08	271.0
   2022	1.68	292.7
   2023	5.02	304.7
   2024	5.14	313.7

   The federal funds rate is what banks charge one another for overnight loans. It is not a savings-account rate, but savings rates tend to follow it. Inflation in a year is the percent change in the CPI from the year before.

2. 1.

   Bo turns to 2023. Which claim about that year does the table best support?

   • The 5.02 percent rate was above price growth of about 4.1 percent, so a saver at that rate kept buying power
   • The rate trailed price growth, as in 2022, so buying power fell again in 2023
   • Savers who held cash from 2021 through 2023 ended ahead of prices, since the 2023 rate beat inflation that year
   • Inflation was 304.7 percent in 2023, far above the 5.02 percent rate
3. 2.

   Esme puts $10,000 in an account that earns each year's average federal funds rate in 2022, 2023 and 2024, with prices measured from 2021. Which statement is best supported?

   • It grows to about $11,227, but keeping pace with prices needs about $11,576, so buying power fell
   • The balance rose 12.3 percent, above the 8.0 percent of 2022, so buying power held
   • It grows to about $11,227 and prices rose just 3 percent in 2024, so buying power rose
   • Buying power fell 15.8 percent, since the saver gained nothing next to the rise in the whole index
4. 3.

   A writer says the Fed raised rates in 2022 and 2023, so inflation fell. Kira tests the claim against the table. What is the best verdict?

   • Cannot be judged, since the table gives an index level and not an inflation rate
   • Contradicted: inflation was already 8.0 percent in 2022, after rates had begun to rise
   • Supported: rates rose from 1.68 to 5.02 and inflation fell from 8.0 to 4.1 percent, so higher rates caused the fall
   • Consistent with the claim but not proof: inflation fell as rates rose, yet other causes are not ruled out

5. Two savers, same yearly return, different timing (example figures, made up for practice)

   Year	Ayo at 7%	Bea at 7%	Ayo at 5%	Bea at 5%
   10	$27,633	$0	$25,156	$0
   20	$54,358	$27,633	$40,976	$25,156
   30	$106,931	$81,991	$66,746	$66,132
   40	$210,349	$188,922	$108,722	$132,878

   Ayo saves $2,000 at the end of each of years 1 to 10, then adds nothing ($20,000 in all). Bea saves $2,000 at the end of each of years 11 to 40 ($60,000 in all). Each balance grows in proportion to the yearly deposit.

6. 4.

   Jun reads the year-40 row at 7 percent. Which statement is best supported?

   • Ayo is ahead mainly because his yearly deposits are larger than Bea's in each of the ten years he saves
   • Ayo is ahead by about $21,400 on $40,000 less saved, since his deposits compounded longer
   • The two are about even, since both earn the same 7 percent a year
   • Bea is ahead, because she saved $60,000 against Ayo's $20,000
7. 5.

   Luz compares the 7 percent columns with the 5 percent columns. Which statement about the year-40 row fits best?

   • Higher returns reward the saver who deposited more dollars, so Bea wins at 7 percent as well
   • Ayo's head start wins at 7 percent but loses at 5, so lower returns reward early money less
   • Starting early wins at any return, since Ayo's money has more time
   • The return hardly matters, since Ayo is ahead at year 30 under both rates

8. Doubling time at four yearly rates (computed for this sheet from compound growth)

   Yearly rate	Rule of 72	Exact time
   1%	72.0 years	69.7 years
   6%	12.0 years	11.9 years
   12%	6.0 years	6.1 years
   36%	2.0 years	2.3 years

   The rule of 72 divides 72 by the yearly rate in percent. The exact time solves (1 + rate) to the power of the years equal to 2, with interest added once a year.

9. 6.

   Milo compares the rule with the exact times. Where is the rule furthest off, as a share of the exact time?

   • At 1 percent: 72.0 against 69.7 years is 2.3 years off, the largest gap in years, so it is least reliable
   • The rule is equally accurate at each rate, since one formula gives each row from the same inputs
   • At 36 percent: 2.0 against 2.3 years is about 11 percent off, but at 6 percent it is under 1 percent off
   • At 12 percent: 6.0 against 6.1 years, since a rule built for one rate is least reliable in the middle
10. 7.

    A planner says $20,000 at 12 percent doubles in 6 years under the rule. Noah finds the balance after exactly 6 years. Which result is right?

    • About $42,000, since compounding makes the exact figure larger than the rule gives
    • Exactly $40,000, since the rule of 72 is exact at 12 percent and 6 years
    • About $34,400, since six years at 12 percent adds 72 percent to $20,000
    • About $39,500, a bit under $40,000, since the exact doubling time is 6.1 years

11. Two accounts and inflation (example figures, made up for practice)

    Account	Yearly interest	Tax on the interest
    A: taxable savings	4.5%	22% each year
    B: tax-free bond fund	3.6%	none

    Prices rise 3.0 percent a year. After-tax return is interest x (1 - tax rate). Real return is about the after-tax return less inflation.

12. 8.

    Ren asks at what tax rate on account A the two accounts would tie after tax. Which answer is best?

    • 22 percent, the rate on the card, since the accounts are already tied at that rate
    • 20 percent: 4.5 x 0.80 is 3.6, so A wins below that rate and B wins above it
    • 0.9 percent, the gap in stated interest, since the tax must remove just that gap
    • 3.6 percent, the interest on B, since A must be taxed down to B's interest rate

13. S&P 500 index, last trading day of each year (S&P Dow Jones Indices via FRED, read Nov 14, 2026)

    Year end	Index level
    2021	4,766.18
    2022	3,839.50
    2023	4,769.83

    The index counts share prices only, not the dividends that its stocks paid. A past return does not promise a future one.

14. 9.

    A brochure says the index averaged 2.4 percent a year in 2022 and 2023. Tala checks the levels. Which statement does the table support?

    • The index ended well below its 2021 level, since the 2022 fall was the bigger of the two moves
    • The index grew 2.4 percent a year, so a $10,000 stake from 2021 would be about $10,500
    • The index gained about 4.8 percent over the two years, since 24.2 less 19.4 is 4.8
    • The changes are -19.4 and +24.2, which average 2.4, yet the index ended 2023 barely above 2021
15. 10.

    Zee must pick the claim about the index that the table cannot support. Which claim is it?

    • The index was nearly flat from the end of 2021 to the end of 2023
    • A stake made at the end of 2023 will grow about 2.4 percent a year
    • The 2023 rise was bigger in percent than the 2022 fall was
    • These levels leave out the dividends paid by the stocks in the index