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The maths

How the numbers work

Every date and amount in Richer Road comes from one monthly calculation. Here it is, with worked examples you can check yourself.

On this page
  1. Your month and your savings goals
  2. Anything you owe: each month, in this order
  3. The order extra money goes
  4. Interest-free and intro rates
  5. How dates are counted
  6. What the estimate leaves out
  7. What if?
  8. Home loan comparison
  9. Worked examples (hypothetical)
  10. How we check it

Your month and your savings goals

  • Left over each month is take-home pay minus spending minus minimum repayments. For $4,200 coming in, $3,400 of spending and $350 of minimums: $4,200 − $3,400 − $350 = $450.
  • A savings goal date is what you still need, divided by what you put aside each month, rounded up to a whole month. For a $5,000 goal with nothing saved yet and $250 a month: $5,000 ÷ $250 = 20 months.
  • Interest you might earn on savings isn’t included, so you may get there a little sooner.

Anything you owe: each month, in this order

  1. Interest is added. Each balance grows by its yearly rate divided by 12. For $5,000 at 20%: $5,000 × 20% ÷ 12 = $83.33.
  2. Minimums are paid. Every debt gets its minimum, or what’s left of it if that’s smaller. Paying $150 leaves $5,083.33 − $150 = $4,933.33.
  3. The rest goes in your order. Your monthly budget is your minimums plus your extra. Whatever is left after the minimums goes to one debt at a time, in the order you chose.
  4. Payments roll on. When a debt is paid off, its minimum stays in your budget and moves to the next debt.

We repeat this, month by month, until every balance reaches zero. The number of months gives your paid-off date; the interest added along the way is your total interest.

The order extra money goes

  • The order you listed: top of your list first.
  • Highest interest rate first (the avalanche method): ties go to the smaller balance.
  • Smallest balance first (the snowball method): by each balance when the plan starts; ties follow your list.
  • Minimums only, shown for comparison: each debt pays only its own minimum, and a paid-off debt’s minimum isn’t reused.

Interest-free and intro rates

If a debt has a lower rate for a set time, the lower rate applies for the months left that you enter, then the normal rate. Update the months left when you update the balance.

How dates are counted

We count your next payment as month 1 and show dates as if it falls next month. If your next payment is due this month, you may finish a month sooner than shown. We’d rather you arrive early than late.

What the estimate leaves out

  • Fees, and rate changes unless you try one in What if?
  • Daily interest. Many lenders charge interest daily rather than monthly, which moves the total by a few cents to a few dollars.
  • Falling minimums. We keep each minimum at the amount you enter. Many card minimums fall as the balance falls; paying the same amount every month, as we assume, clears a debt sooner.
  • New spending on the debts in your plan.

What if?

  • Extra money comes in: the amount is added to month 1’s budget and goes to your debts in your order.
  • Buying on credit: the price is added to that debt’s balance today.
  • A tough few months: your extra stops for those months; minimums are still paid.
  • A rate change: the new rate applies from month 1.

Home loan comparison

All three start from the same pay, living costs and repayment, with nothing already saved. “Left over” is your take-home pay minus living costs minus the repayment. Months have 30 days.

  • Extra repayments: the left-over amount goes onto the loan at the end of each month.
  • Offset account: pay lands in the offset, living costs come out evenly through the month, and interest is charged on the loan balance minus the average offset balance. The loan counts as cleared when the offset covers it.
  • Velocity banking: when the line of credit is at zero, a lump moves from it onto the loan. Pay goes into the line of credit, and the repayment and living costs come out of it. Its interest is charged on its average daily balance. If it would go over its limit, the plan is shown as not working.

Fees, tax and rate changes aren’t included. The comparison is general information that shows how each set-up works on the numbers entered. It isn’t a recommendation of any loan, account or line of credit. Before choosing one, consider advice from a licensed financial adviser or mortgage broker.

Worked examples (hypothetical)

These are hypothetical examples that show the method, not predictions. Amounts work in any currency; we use $ here. Months count from your next payment.

One debt, the same payment every month

Debt and paymentMonths to clearTotal interest
$5,000 at 20%, paying $15050 (4 years 2 months)$2,359.09
$5,000 at 20%, paying $25025 (2 years 1 month)$1,133.03
$10,000 at 8%, paying $30038 (3 years 2 months)$1,346.95
$25,000 at 6.5%, paying $50059 (4 years 11 months)$4,234.89
$1,200 at 29.99%, paying $6029 (2 years 5 months)$484.05
$3,000 at 14%, paying $10038 (3 years 2 months)$713.99
$2,000 at 0%, paying $10020 (1 year 8 months)$0.00
$8,000 at 24%, paying $150Never: interest is $160 a month—

An interest-free start

Debt and paymentMonths to clearTotal interest
$2,400 at 0% for 6 months, then 19.99%, paying $20013 (1 year 1 month)$75.18
$2,400 at 0% for 12 months, then 19.99%, paying $20012 (1 year)$0.00

Three debts, four orders

Credit card $6,400 at 21.9%, minimum $190. Car loan $14,800 at 8.4%, minimum $360. Personal loan $3,200 at 14%, minimum $120. Extra $250 a month, so the monthly budget is $920.

OrderFirst debt clearedMonths to clear allTotal interest
Your order (card, car, personal loan)Credit card, month 1831 (2 years 7 months)$3,791.49
Highest interest rate firstCredit card, month 1831 (2 years 7 months)$3,741.79
Smallest balance firstPersonal loan, month 1031 (2 years 7 months)$3,987.10
Minimums onlyPersonal loan, month 3353 (4 years 5 months)$6,990.94

Two debts, two orders

Debt A $1,000 at 10%, Debt B $4,000 at 22%, minimums $25 each, $250 a month in total.

OrderFirst debt clearedMonths to clear allTotal interest
Highest interest rate firstDebt B, month 2225 (2 years 1 month)$1,041.81
Smallest balance firstDebt A, month 525 (2 years 1 month)$1,242.49

What if? On the three debts, highest rate first

Starting point: 31 months and $3,741.79 interest.

ChangeMonths to clear allTotal interestDifference
$1,000 extra in month 129 (2 years 5 months)$3,269.042 months sooner, $472.75 less
$500 bought on the credit card today32 (2 years 8 months)$4,016.251 month later, $274.46 more
Minimums only for the first 3 months32 (2 years 8 months)$4,117.171 month later, $375.38 more
Credit card rate falls to 12%30 (2 years 6 months)$3,067.501 month sooner, $674.29 less

A home loan, three set-ups

Loan $420,000 at 6.2%, repayment $2,700 a month. Take-home pay $9,500 and living costs $4,800 a month, so $2,000 is left over. Line of credit at 9.5%, limit $30,000, $15,000 moved each time.

Set-upMonths to clearTotal interest
Repayments only316 (26 years 4 months)$433,025.76
Extra repayments121 (10 years 1 month)$144,858.54
Offset account120 (10 years)$141,169.05
Velocity banking120 (10 years)$143,526.94, including $3,788.15 on the line of credit

How we check it

Every example on this page is worked out by the same code as your plan, then again by a second model written separately in another programming language. They agree to the cent. Any loan calculator that adds interest monthly will match the one-debt examples.

Spotted something that looks wrong? Tell us. Fixes are listed in our corrections log.

What’s left each month?

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