Saving and investing: interest, compounding, risk and return
Grade 12 Social Studies Worksheet - Challenge Me
Circle the best answer.
Read this first
$10,000 in two funds that each earn 7.0 percent before fees (example figures, made up for practice)
Year Fund P (fee 0.1% a year) Fund Q (fee 1.1% a year) 10 $19,488 $17,740 20 $37,980 $31,472 30 $74,017 $55,831 Each fee is taken from the balance every year. A brochure for fund Q (made up) says: "Just one percent more in fees. You will never notice it."
Bo asks what share of fund P's 30-year gain fund Q's higher fee takes away. Which answer fits the table?
- About 28 percent: Q's gain is $45,831 against $64,017 for P, far more than 1.0 percent
- About 25 percent, because Q's final balance is 25 percent lower than P's final balance
- About $18,186, which is the gap in dollars and is the share lost
- About 1 percent, because the fee difference is 1.0 percent a year
Esme wonders why a 1.0 percent fee has such a large effect over 30 years. Which explanation fits the table?
- The fee comes out of a balance that would itself have compounded, so each year's loss also loses later growth
- Fund Q earns less than 7.0 percent before fees, so the gap has nothing to do with the fee
- The fee rate rises each year, so by year 30 fund Q is charging far more than 1.1 percent
- The fee is subtracted from the 7.0 percent as a flat amount in dollars, which hurts a small balance the most
Use this
Card A, "Two funds" (made up). Harbor is a stock fund; Summit is a bond fund. Table, columns Scenario | Chance | Harbor | Summit | Half and half: Boom | 25% | +30% | +2% | +16%; Normal | 50% | +10% | +4% | +7%; Recession | 25% | -20% | +7% | -6.5%. Half and half puts equal amounts in each fund. Chances and returns are example figures, made up for practice.
Kira weighs the half-and-half mix against Harbor alone. Which statement does card A best support?
- The mix earns the same 5.875 percent in every scenario, the average of the two funds
- The mix adds nothing, since each of its returns sits between the two funds' returns
- The mix cuts the worst case from -20 to -6.5 percent but gives up return, about 5.9 against 7.5
- The mix beats both funds in every scenario, so it is the better choice for any kind of saver at all
Luz asks which feature of card A explains why the mix lowers the risk. Which is it?
- In the recession row Summit rises while Harbor falls, so part of the loss is offset
- The mix holds more bonds than stocks, so it behaves like Summit
- Summit has the higher expected return, which lifts the mix above Harbor
- Both funds have positive returns in two of three scenarios, so the mix cannot lose money
Milo imagines Summit also fell 10 percent in a recession, as Harbor falls 20. What would that do to the mix?
- It would lose 10 percent, since the mix takes the smaller of the two losses
- It would lose 15 percent in a recession; the protection comes from funds moving apart
- Owning two funds would add no protection in any scenario, since the funds are unrelated
- It would stay at -6.5 percent, since the mix return is fixed by the equal weights
Noah checks the 7.5 percent expected return for Harbor. Which missing fact would most change the case for the mix?
- Whether the funds are insured by the FDIC, since insured funds cannot lose
- Whether recessions are likelier than the listed 25 percent, which would pull Harbor's average down
- How many scenarios the table lists, since three scenarios cannot describe a market
- Whether Harbor and Summit charge the same fees, since fees are the main cost of owning a fund today
Use this
Card A, "Two accounts" (made up). Account X pays 6 percent a year, compounded monthly. Account Y pays 6.1 percent a year, compounded once a year. Card B, "Effective annual yield" (in our words). The effective annual yield is the growth in one year after compounding. Account X's is about 6.17 percent (1.005 to the 12th power is about 1.0617). Account Y's is 6.1 percent. Card C, "An ad" (made up). "At 6 percent, your savings double in 12 years." Card D, "An assumption" (made up). Suppose prices rise 3 percent a year for as long as the savings grow. Card E, "The rule of 72" (in our words, not a quotation). Dividing 72 by a yearly growth rate in percent gives a rough number of years to double.
Pia compares accounts X and Y using cards A and B. Which statement is best supported?
- X is better by a wide margin, because monthly compounding adds a full point a year to the yield
- Y is better, because its stated rate of 6.1 percent is higher than X's 6 percent
- X is better: monthly compounding gives about 6.17 percent a year, above Y's 6.1 percent
- They are equal, because 6 percent and 6.1 percent are too close to tell apart
Ren reads the ad on card C alongside card D. Which statement is best supported?
- The claim is about right in dollars, 12 years, and buying power doubles in about 12 years too
- In dollars the claim is about right, 12 years, but buying power doubles only in about 24 years
- The claim holds for buying power too, since inflation hits every account equally and cancels out
- Buying power doubles in about 8 years, since 72 divided by 6 plus 3 is 8
Tala applies the rule of 72 to accounts X and Y. Which statement about doubling times is best supported?
- The rule cannot be used for X, since it is meant for yearly compounding
- X doubles in 12 years and Y in 11.8, so Y is faster because its stated rate is higher
- They barely differ: 72 / 6.17 is about 11.7 years and 72 / 6.1 about 11.8
- Monthly compounding cuts X's doubling time to about 6 years, half of Y's
A writer says, "Since 6 percent beats the 3 percent in card D, you can spend the interest each year and never lose buying power." Zee tests it. What is the verdict?
- Not supported, since a 6 percent rate is a promise on just the first dollar saved in each year
- Not supported: spending the interest leaves the balance flat while prices rise 3 percent a year
- Supported: a positive real return means the interest is safe to spend
- Supported for the first year, and then the balance outgrows prices