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."
Ari tests the brochure against the table. What is the best verdict?
- Not supported: the extra 1.0 percent a year cuts the 30-year balance by about a quarter
- Supported: 1.0 percent of $10,000 is just $100 a year, which no saver would ever notice or miss
- Supported: at year 10 the gap is just $1,748, small next to the $10,000 invested
- Not supported: Fund Q's balance is higher than fund P's in each year shown
Esme wonders why a 1.0 percent fee has such a large effect over 30 years. Which explanation fits the table?
- The fee is subtracted from the 7.0 percent as a flat amount in dollars, which hurts a small balance the most
- 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
Jun looks for the missing evidence that most limits what the table shows about funds P and Q. Which is it?
- How many dollars each fund holds in total, because a larger fund must be better
- The average inflation rate over the 30 years, because it changes which fund is ahead after costs are counted
- Whether each fee is taken monthly or yearly, because that decides which fund wins
- Whether Q earns more before fees, which could offset its cost; the table assumes both earn 7.0 percent
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 cuts the worst case from -20 to -6.5 percent but gives up return, about 5.9 against 7.5
- The mix earns the same 5.875 percent in every scenario, the average of the two funds
- The mix beats both funds in every scenario, so it is the better choice for any kind of saver at all
- The mix adds nothing, since each of its returns sits between the two funds' returns
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
- Both funds have positive returns in two of three scenarios, so the mix cannot lose money
- Summit has the higher expected return, which lifts the mix above Harbor
Noah checks the 7.5 percent expected return for Harbor. Which missing fact would most change the case for the mix?
- Whether Harbor and Summit charge the same fees, since fees are the main cost of owning a fund today
- Whether the funds are insured by the FDIC, since insured funds cannot lose
- How many scenarios the table lists, since three scenarios cannot describe a market
- Whether recessions are likelier than the listed 25 percent, which would pull Harbor's average down
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: monthly compounding gives about 6.17 percent a year, above Y's 6.1 percent
- 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
- 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 holds for buying power too, since inflation hits every account equally and cancels out
- 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
- 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?
- They barely differ: 72 / 6.17 is about 11.7 years and 72 / 6.1 about 11.8
- X doubles in 12 years and Y in 11.8, so Y is faster because its stated rate is higher
- Monthly compounding cuts X's doubling time to about 6 years, half of Y's
- The rule cannot be used for X, since it is meant for yearly compounding
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: spending the interest leaves the balance flat while prices rise 3 percent a year
- Supported for the first year, and then the balance outgrows prices
- Not supported, since a 6 percent rate is a promise on just the first dollar saved in each year
- Supported: a positive real return means the interest is safe to spend