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.
Bo sees Dara's yearly interest stay at $50. What best explains why Eli's yearly interest grows?
- Eli adds new money each year, so his balance climbs faster than Dara's
- Eli's interest is paid twice a year, so he gets two chances to earn on the same balance in each year of the table
- Eli's bank raises his rate each year, so he earns a higher percent than Dara
- Eli earns interest on his earlier interest as well as on his deposit, so each year's base gets bigger
Esme compares the year-30 row of the table. Which statement about it is best supported?
- Eli's balance is about 1.7 times Dara's, $4,322 against $2,500
- Eli's balance is $1,822 higher because he saved $1,822 more than Dara did
- Eli's balance is about double Dara's, since compounding doubles simple interest
- Eli's balance is about 73 percent of Dara's, since $4,322 is smaller than $2,500 plus interest
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.
The stock fund Mina bought through the bank loses $8,000 in value. Luz asks what card B says about getting that back.
- 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
- The FDIC repays it, because the fund is a separate ownership category with its own $250,000 limit
Milo compares Ravi's 2 percent savings with Sol's fund that averages 8 percent. Which statement does card A support?
- Ravi's doubles in about 36 years and Sol's in about 9, and the 8 percent average is guaranteed
- Ravi's doubles in about 18 years and Sol's in about 4.5, since the rule uses half the rate
- Both double in about 9 years, since the rule only depends on the starting amount
- Ravi's money doubles in about 36 years and Sol's in about 9, if each rate held every year
Noah notes that card A calls the rule of 72 an estimate. Which use of it is most reliable?
- Finding the doubling time at 1 percent: exactly 72 years
- Guessing the doubling time at 8 percent: about 9 years
- Finding the doubling time at 40 percent: about 1.8 years
- Finding a balance after 12 years at 6 percent to the nearest dollar
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 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
- The bond fund, because its middle return and risk fit any goal
Ren helps Ana, who is 20, plan for retirement at 65. Which statement fits the table?
- The savings account fits, since 45 years of 1 percent cannot lose and it is fully insured
- 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
Tala follows a $10,000 stock fund that loses 30 percent one year, then gains 30 percent the next. Where does it end?
- Below its start, at $9,100, because the 30 percent gain is figured on the smaller $7,000
- 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
Zee writes one claim from the table. Which claim does it best support?
- The stock fund gained about 7 percent in each of the years it was held, with no losses at all
- In these three examples, the choice with the higher average also has the deeper worst year
- The savings account is the best choice for everyone, since it is insured
- A higher average return always comes with a worse worst year, in every investment