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Learn through experiments

Trace a loan balance

When does making a payment still leave more debt?

Entering midway? Revisit Budget for timing and surprises for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

An original fictional loan applies a monthly interest rate to the opening balance, then takes a payment capped at the amount owed. No fees or annual-rate conversion is hidden.

Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.

Go directly to the experiment · Review basic mathematics

2 · Predict

What do you expect?

Predict what happens if the monthly payment is smaller than interest.

3 · Experiment

Change one thing. Inspect what happens.

  1. For 500 at 2%, calculate first interest and remaining balance after 60 payment.
  2. Set a large balance and a small payment; inspect growing debt.
  3. Set interest to zero, then choose a payment that finishes the loan. Verify the final payment is capped.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Remaining debt184.594 credits
Payments made360 credits
Interest accrued44.594 credits

Compare the current results

Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.
0450
  • Month 1 remaining credits450
    Month 1 remaining credits: 450Horizontal bar from zero to 450, on the shared zero to 450 numeric axis.
  • Month 2 remaining credits399
    Month 2 remaining credits: 399Horizontal bar from zero to 399, on the shared zero to 450 numeric axis.
  • Month 3 remaining credits346.98
    Month 3 remaining credits: 346.98Horizontal bar from zero to 346.98, on the shared zero to 450 numeric axis.
  • Month 4 remaining credits293.92
    Month 4 remaining credits: 293.92Horizontal bar from zero to 293.92, on the shared zero to 450 numeric axis.
  • Month 5 remaining credits239.798
    Month 5 remaining credits: 239.798Horizontal bar from zero to 239.798, on the shared zero to 450 numeric axis.
  • Month 6 remaining credits184.594
    Month 6 remaining credits: 184.594Horizontal bar from zero to 184.594, on the shared zero to 450 numeric axis.

Follow the calculation

  1. Month 1: interest 10, payment 60, remaining 450.
  2. Month 2: interest 9, payment 60, remaining 399.
  3. Month 3: interest 7.98, payment 60, remaining 346.98.
  4. Month 4: interest 6.9396, payment 60, remaining 293.9196.
  5. Month 5: interest 5.8784, payment 60, remaining 239.798.
  6. Month 6: interest 4.796, payment 60, remaining 184.594.

Interest is charged on the preceding balance before payment. A payment below the interest charge increases debt. Monthly rate is not an annual rate.

Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.

4 · Understand

Explain the mechanism

Trace a loan balance

An original fictional loan applies a monthly interest rate to the opening balance, then takes a payment capped at the amount owed. No fees or annual-rate conversion is hidden.

Predict before changing inputs

Predict what happens if the monthly payment is smaller than interest.

Understand the mechanism

Interest pays for use of the outstanding balance. Applying it before payment is the explicit timing convention here.

First month at defaults: interest 500×0.02=10, payment 60, ending balance 450. Second interest is 9 because the balance changed.

When payment is less than interest, the unpaid amount adds to debt. A stated monthly percentage cannot be treated as the same annual percentage.

Calculate it yourself

Interest = opening balance × monthly rate; actual payment = min(planned payment, balance + interest); next balance = balance + interest − payment.

Guided investigation

  1. For 500 at 2%, calculate first interest and remaining balance after 60 payment.

  2. Set a large balance and a small payment; inspect growing debt.

  3. Set interest to zero, then choose a payment that finishes the loan. Verify the final payment is capped.

Assumptions and limitations

  • No fees, compounding within a month, penalties or changing rates.

  • Fictional comparison only; actual contracts and affordability require additional information.

Further investigations

High school: Make a three-payment table and separate principal from interest.

College: Derive the fixed-payment formula and verify against an iterative schedule.

Working professionals: Compare fictional financing offers using full cash flows and omitted-cost notes.

5 · Apply

Try a fresh case

A new 200-credit loan has 3% monthly interest and a 50-credit first payment. What remains after one month?

This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.

Take the investigation further

Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.

School investigation

Make a three-payment table and separate principal from interest.

College investigation

Derive the fixed-payment formula and verify against an iterative schedule.

Workplace investigation

Compare fictional financing offers using full cash flows and omitted-cost notes.

6 · Continue

Keep the evidence, choose your next step

Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.