It Cuts Both Ways: Debt Compounds Too

In step 3 you saw time bend savings upward. Now point that exact same engine at a credit-card balance and watch it bend the other way.

3 quick questions · about 2 min · no sign-up

Question 1 of 3

A credit card charges 24% APR and compounds monthly. You carry a $1,000 balance and pay nothing for a year. The interest works the same exponential way your savings did in steps 2-3 — just aimed at you. What's the monthly rate it grows by?

• 2% per month
• 24% per month
• 0.24% per month
• I'm not sure

You said: 2% per month

Right. 24% APR split across 12 months is 24 ÷ 12 = 2% each month. It's the identical setup from step 2 — a fixed periodic rate applied over and over — only now the balance is yours to pay, not yours to keep.

You said: 24% per month

That's the yearly rate, not the monthly one. APR means annual rate, so you divide across the 12 compounding periods: 24 ÷ 12 = 2% per month. Same per-period logic you used for savings, pointed the other way.

You said: 0.24% per month

You divided by 100 instead of by 12. 24% APR over 12 months is 24 ÷ 12 = 2% per month. That small-looking 2%, compounded, is exactly the engine that made savings explode upward.

You said: I'm not sure

It's 2% per month. APR is the annual rate, so you spread it across the 12 compounding periods: 24 ÷ 12 = 2%. Same fixed periodic rate as your savings example, just charged to you instead.

So it's 2% a month, compounding — the same machine as before. Let's run it for a year and see where $1,000 lands.

Question 2 of 3

Your $1,000 grows by 2% every month for 12 months, each month's interest charged on the new larger balance. A flat 24% would be $240 in interest. With monthly compounding, how much interest do you actually owe?

• About $268
• Exactly $240
• About $500
• I'm not sure

You said: About $268

Exactly. 1000 × (1.02)^12 = $1,268.24, so about $268 in interest — $28 more than the flat $240. That extra $28 is interest charged on earlier interest, the same 'interest on interest' that grew your savings, now working against you.

You said: Exactly $240

$240 is the flat-rate answer, but compounding charges interest on interest each month, so you owe more: 1000 × (1.02)^12 = $1,268.24, about $268. The $28 gap IS the compounding — the same bend you saw in savings.

You said: About $500

Too high for one year. 1000 × (1.02)^12 = $1,268.24, so roughly $268 in interest — a bit above the flat $240. The compounding gap is real but modest over 12 months; it's the LATER years where it gets brutal.

You said: I'm not sure

It's about $268. Run the same formula as savings: 1000 × (1.02)^12 = $1,268.24. That's $28 more than a flat 24% ($240), and that extra is interest piling onto interest — compounding aimed at you.

Modest in year one, but the bend steepens. Now apply the whole idea: what does it mean for someone carrying a balance for years?

Question 3 of 3

Same card, 2%/month, but now the balance sits unpaid for 3 years instead of 1. Using the exact engine from steps 2-3, what happens to the $1,000?

• It roughly doubles — about $2,040 — because each year's interest compounds on a bigger and bigger balance
• It triples to about $1,720, since 24% × 3 years = 72%
• It grows a little — to about $1,300 — since 3 years isn't that long
• I'm not sure

You said: It roughly doubles — about $2,040 — because each year's interest compounds on a bigger and bigger balance

That's it. 1000 × (1.02)^36 = $2,039.89. The curve bends upward over time exactly like savings did in step 3 — but here the growth is debt you owe. One mechanic, two outcomes: it builds wealth or it builds a trap.

You said: It triples to about $1,720, since 24% × 3 years = 72%

Multiplying the flat rate ignores compounding — and 72% of $1,000 is $720, not a triple anyway. The real engine is 1000 × (1.02)^36 = $2,039.89. It roughly DOUBLES, because interest keeps stacking on interest, just like your savings curve.

You said: It grows a little — to about $1,300 — since 3 years isn't that long

That's closer to the one-year figure. Over 36 months the bend steepens: 1000 × (1.02)^36 = $2,039.89, roughly double. Time is the engine here too — the same upward curve from step 3, now growing what you owe.

You said: I'm not sure

It roughly doubles to about $2,040. Same formula as savings: 1000 × (1.02)^36 = $2,039.89. Carried long enough, a balance bends upward exactly the way your savings did — only now the curve is pointed at your net worth.

The takeaway

Compound interest doesn't care which side of the ledger it's on: the same 2%-a-month engine that grew your savings doubles an unpaid credit-card balance in about 3 years. One mechanic builds wealth for you or builds a trap against you — direction is the only difference.

The pattern

You now hold the one idea that unifies all of personal finance math: interest computed on a growing balance compounds, which makes both savings and debt grow exponentially rather than linearly — so time and starting point matter more than most people expect, and the same force that builds wealth in an index fund detonates an unpaid credit-card balance. You can read a rate-and-balance situation and predict roughly which way the curve bends and how fast. From here, a tutor can take you into the real numbers that run your life: how compounding frequency (daily vs. monthly vs. annual) changes outcomes, how to read an APR vs. APY, the Rule of 72 for quick mental estimates, and how to model your own 401(k) or debt-payoff timeline. Bring a real number you care about and let's make it concrete.