The pile Maya owes grows faster each year when she pays nothing.
The big ideaInterest on a loan compounds too: unpaid, the pile owed grows faster each year.
How it works
Maya borrowed one hundred pretend coins from Mr. Moss. Each year the barn added one new coin for every ten coins owed.
Unpaid, the pile grows faster every year, because the interest is charged on the interest already owed. After ten years Maya owes 256, more than double.
Paying sooner is cheaper, and paying a little each year slows the snowball until it is gone.
The longer Maya waits to pay it all back, the more extra she pays.Paying 30 coins a year, the pile is gone in year 5.
Example 1: How much interest next year?
The barn adds 1 coin for every 10 coins owed.
Maya owes 121 coins.
121 holds twelve tens, and 12 × 10 = 120.
So 12 coins are added.
Example 2: Pay back after one year
Maya owes 100, and one year adds 10 coins.
100 + 10 = 110
The extra she pays is 110 − 100 = 10 coins.
Example 3: Pay back after three years
After 3 years unpaid, the pile is 133.
133 − 100 = 33
That is 33 coins extra, against only 10 for paying after one year.
Example 4: Paying 30 a year
Year 1: she owes 110, pays 30, and 110 − 30 = 80.
Year 2: 80 holds eight tens, so 80 + 8 = 88, and 88 − 30 = 58.
Year 3: 58 holds five tens, so 58 + 5 = 63, and 63 − 30 = 33.
Year 4: 33 holds three tens, so 33 + 3 = 36, and 36 − 30 = 6.
Year 5: she pays the last 6, and the pile is gone. She paid 30 + 30 + 30 + 30 + 6 = 126 coins in all.
Still owed after each payment.
Words to know
borrower
The one who owes the coins.
lender
The one who lends the coins, like Mr. Moss.
interest
Extra coins added to what is owed.
snowball
A pile owed that grows faster each year.
Watch out
Interest on interest owed makes the pile grow faster every year.
Waiting costs more: after one year the extra is 10, after five years it is 60.
Paying a little each year slows the snowball.
These loans are made up. Real loans use different numbers, so ask a grown-up how theirs work.
Try it
Maya owes 133 coins. How many coins of interest are added next year?
A hundred coins owed, unpaid for one year, becomes how many?
Does paying back after one year or after five years cost less extra?
Interest on an unpaid loan: does it work for you or against you?
Answers: 1. 13 coins · 2. 110 coins · 3. After one year · 4. Against you
Try at homeWith a grown-up, talk about what it costs to borrow, in a made-up story and in real life. What do they ask before they borrow? Why does the time to pay back matter?
For grown-upsThe same snowball can roll for you or against you. Talk about what a grown-up asks before borrowing: what it costs and when it must be paid back. These numbers are made up, and real loans differ, so look at any real loan's terms together.
Open these notes on screenScan the code, or go to tutorpip.com.