Interest is really "rent on money"
You borrow a friend's drill for a week and buy them a bubble tea as thanks when you return it. Borrowing something costs a little something—that feels natural.
Flip it around: putting money in the bank is like "renting" your money to the bank to use, and the bank pays you interest. So an interest rate is both the cost of borrowing and the reward for saving.
Simple vs. compound interest: does interest earn more interest?
Simple interest: interest is figured only on the original principal. With 100 yuan at 10% a year, that's a fixed 10 yuan each year. After three years, 30 yuan total.
Compound interest: last period's interest is folded back into the principal, so the next period earns on the whole thing. Year one grows to 110; year two earns 10% on 110 to reach 121; year three earns on 121 to reach about 133.
The Rule of 72: doubling time in your head
Want a rough sense of "how many years it takes money to double under compounding"? There's a handy estimate: divide 72 by the annual percentage rate.
For example, at 6% a year, 72 ÷ 6 = 12, so about 12 years to double; at 8%, 72 ÷ 8 = 9, about 9 years. The higher the rate, the faster it doubles.
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The lesson compares an "interest rate" to a cost of borrowing money, calling it the "____ on money." Fill in the blank.
答案：rent
An interest rate is likened to "rent on money"—using someone else's money costs a proportional fee.
You borrow 100 yuan and agree to repay 5 yuan extra after a year. What's the interest rate here?
答案：5%
The extra 5 yuan relative to the 100 yuan principal is 5 ÷ 100 = 5%.
True or false: The core difference between compound and simple interest is that compounding folds the interest you've already earned back into the principal, so interest earns more interest.
答案：True
Exactly: compounding lets interest take part in the next round of interest, while simple interest only counts the original principal.
Principal of 100 yuan at 10% a year. Under compounding, roughly how much is it at the end of year two?
答案：121 yuan
Year one 100 → 110; year two takes another 10% on 110 to reach 121. That's 1 yuan more than simple interest's 120, and that 1 yuan is "interest earned on interest."
Using the Rule of 72: at roughly 6% a year, about how many years does it take the principal to double?
答案：About 12 years
72 ÷ 6 = 12, so about 12 years to double. This is an estimate, not an exact figure.
The Rule of 72 works like this: take 72 and "____" it by the annual percentage rate, and you get the approximate doubling time. Fill in the operation.
答案：divide
72 ÷ annual percentage rate ≈ doubling time. For example, 72 ÷ 8 ≈ 9 years.