Saving and investing: interest, compounding, risk and return
Grade 12 Social Studies Worksheet - Building Confidence
Circle the best answer.
Read this first
Two savers start with $1,000 (example figures, made up for practice)
Year Dara (simple 5%) Eli (compound 5%) 0 $1,000 $1,000 5 $1,250 $1,276 10 $1,500 $1,629 20 $2,000 $2,653 30 $2,500 $4,322 Dara earns 5 percent of her original $1,000 each year ($50) and it is paid out, not reinvested. Eli earns 5 percent of his whole balance once a year and it stays in his account. Neither adds new money.
Ari compares the two columns for years 5 and 10. Which statement does the table support?
- Dara's account stops growing after year 10, while Eli's keeps going well beyond it
- Dara is ahead early on, and Eli passes her after year 10
- Eli's lead grows over time: $26 ahead at year 5 and $129 ahead at year 10
- Eli's lead is steady: he is about $26 ahead at each check-in
Esme compares the year-30 row of the table. Which statement about it is best supported?
- Eli's balance is about 73 percent of Dara's, since $4,322 is smaller than $2,500 plus interest
- Eli's balance is about double Dara's, since compounding doubles simple interest
- Eli's balance is $1,822 higher because he saved $1,822 more than Dara did
- Eli's balance is about 1.7 times Dara's, $4,322 against $2,500
Jun sees Dara's balance hit $2,000 in year 20. Which statement about when Eli's balance reaches $2,000 does the table support?
- Exactly at year 15, halfway between the two rows that bracket $2,000
- At year 10, since $1,629 is close to double the $1,000 he started with, as the table shows
- Between years 10 and 20, since $1,629 is under $2,000 and $2,653 is over it
- Also at year 20, since both savers earn the same 5 percent rate
Use this
Card A, "The rule of 72" (in our words, not a quotation). Dividing 72 by a yearly rate in percent gives a rough number of years for a balance to double at that rate. It is an estimate that works best for rates of about 6 to 10 percent. Card B, "Deposit insurance" (in our words, from the FDIC). Deposits in an insured bank are covered up to $250,000 per depositor, per insured bank, per ownership category. Stocks, bonds and mutual funds are not insured by the FDIC, even when bought through a bank. Card C, "Mina (made up)". Mina has $300,000 in one savings account at one insured bank, in her name alone. She also holds a $40,000 stock mutual fund that she bought through the same bank.
Kira reads cards B and C. Mina asks whether the FDIC covers her $300,000 savings account. Which is the best advice?
- Not all: $250,000 is covered and $50,000 is not, unless some moves to another insured bank
- All of it: she can open a second savings account at the same bank in her own name
- Less than $250,000, because the $40,000 fund also counts toward her limit
- All of it: FDIC insurance covers every deposit account up to the bank's total deposits, however large the balance
The stock fund Mina bought through the bank loses $8,000 in value. Luz asks what card B says about getting that back.
- The FDIC repays it, because the fund is a separate ownership category with its own $250,000 limit
- Nothing: stocks and mutual funds are not insured by the FDIC, even when bought through a bank
- The FDIC repays up to $250,000 of fund losses, since the fund total is just $40,000
- The FDIC repays it, because she bought the fund through an insured bank
Milo compares Ravi's 2 percent savings with Sol's fund that averages 8 percent. Which statement does card A support?
- Both double in about 9 years, since the rule only depends on the starting amount
- Ravi's doubles in about 36 years and Sol's in about 9, and the 8 percent average is guaranteed
- Ravi's money doubles in about 36 years and Sol's in about 9, if each rate held every year
- Ravi's doubles in about 18 years and Sol's in about 4.5, since the rule uses half the rate
Use this
Three example places for savings (example figures, made up for practice). Columns: Choice, Average yearly return, Worst single year, Insured by the FDIC. Savings account, 1%, 0%, Yes, up to the limit; Bond fund, 3%, -4%, No; Stock fund, 7%, -30%, No. These are example rates. Real investments do not guarantee an average or a worst year.
Pia needs $4,000 for a laptop in six months. Which choice does the table support?
- The bond fund, because its middle return and risk fit any goal
- The savings account: lowest return, but no loss to fear when the money is needed soon
- The stock fund, because its -30 percent year is just one year and cannot happen in six
- The stock fund, because its 7 percent average beats the other two in six months
Ren helps Ana, who is 20, plan for retirement at 65. Which statement fits the table?
- The bond fund fits, since it has the same deepest loss as the stock fund
- The stock fund is certain to beat the savings account over 45 years
- A long wait lets Ana recover from a -30 percent year, so the stock fund's higher average fits
- The savings account fits, since 45 years of 1 percent cannot lose and it is fully insured
Tala follows a $10,000 stock fund that loses 30 percent one year, then gains 30 percent the next. Where does it end?
- At $7,900, because the gain is 30 percent of the $3,000 that was lost
- At $10,700, because the stock fund averages 7 percent a year and the table gives that average
- Back at $10,000, because a 30 percent loss and a 30 percent gain cancel out
- Below its start, at $9,100, because the 30 percent gain is figured on the smaller $7,000
Zee writes one claim from the table. Which claim does it best support?
- The savings account is the best choice for everyone, since it is insured
- In these three examples, the choice with the higher average also has the deeper worst year
- A higher average return always comes with a worse worst year, in every investment
- The stock fund gained about 7 percent in each of the years it was held, with no losses at all
