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What a loan costs

The EMI on a loan, the interest paid over its life, a flat rate against a reducing one, and how much a monthly budget can really borrow.

  • Money
  • Untimed
  • Endless levels

How it plays

Each question is a loan repaid in equal monthly instalments on a reducing balance — the convention is stated every time: the yearly rate ÷ 12, charged each month on what is still owed.

The EMI itself, P·r·(1 + r)^n ÷ ((1 + r)^n − 1), is asked as a choice among options at least 4% apart, or typed within 1%. Later kinds ask the total interest, the first instalment's split, which of two loans is cheaper — a flat rate among them — the cost of a longer term, and what a budget can borrow. The sums grow without end.

The wrong options are the real slips: a flat rate computed for a reducing one, the total paid given for the interest, the yearly rate charged monthly. Rates are illustrative, not any lender's; the money is in the currency you pick.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This makes the arithmetic of loans of these kinds quicker and surer. It is not financial advice and claims nothing wider.

Learn

How to get better at what a loan costs: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Turn the yearly rate into a monthly one by dividing by 12, and the years into months by multiplying by 12. Every loan here charges the monthly rate on what is still owed.
  2. Read what is asked: the instalment, the interest, the part of one instalment that repays the loan, or what a payment can borrow. Several wrong options are right answers to the neighbouring question.
  3. Before working anything, bracket the answer with quick bounds (below). With options at least 4% apart, the bounds often leave one or two candidates.
  4. Then compute: the EMI from its formula, totals from EMI × months, and the borrowing from the payment times the annuity factor.

Techniques and tricks

  • Bracket the EMI

    The EMI is more than the loan ÷ months and more than one month’s interest on the whole loan, but less than those two added together.

    e.g. 100,000 at 12% for 5 years: 1,667 and 1,000, so the EMI is between 1,667 and 2,667. It is 2,224.

  • Loan ÷ months, plus part of the interest

    For a close estimate, add to loan ÷ months a share of one month’s interest: about 55% for terms up to 5 years, about 60% at 10 years, and two thirds or more at 20 to 30 years.

    e.g. 100,000 at 12% for 5 years: 1,667 + 0.55 × 1,000 ≈ 2,217; the EMI is 2,224.

  • The first instalment splits by one month’s interest

    The interest in the first EMI is the whole loan × the yearly rate ÷ 12. The rest of the EMI repays the loan.

    e.g. 100,000 at 12%: 1,000 of the first EMI is interest.

  • Total interest is all you pay less the loan

    Multiply the EMI by the number of months and take away the sum borrowed. The same sum is repaid either way, so the difference between two loans’ totals is all interest.

  • A flat rate is nearly double

    A flat rate charges interest on the whole loan every year. Over 3 to 10 years it costs about as much as a reducing rate 1.6 to 1.9 times as high: higher multiples for short loans, lower for long ones.

    e.g. Flat interest is just loan × rate × years: 100,000 at 6% flat for 5 years is 30,000.

  • Borrowing from a payment

    What a monthly payment can borrow is the payment × (1 − (1 + r)^−n) ÷ r, with r monthly. It is always much less than the payment × months.

    e.g. 10,000 a month for 10 years at 9% borrows about 789,417, not 1,200,000.

As the levels climb

  • The kinds unlock in this order: the EMI at level 0; total interest and the first instalment at level 1; which loan costs less at level 3; the cost of a longer loan and how much you can borrow at level 5.
  • Between unlocks, and for ever after, the loans grow: bigger sums, terms up to 30 years for the EMI, and from size 3 rates with a half per cent. Long terms raise the share of the month’s interest in the EMI, so use the larger shares.
  • In “Which loan costs less”, one loan has a lower rate or a flat rate, but not every advantage. Work both totals; the answer is not always the one with the lower number.
  • Bigger sums give a little more time, 8% more per notch for the first twelve. Use it to work both loans fully rather than guessing from the rates.

Traps to avoid

  • A flat rate computed for a reducing one: (loan + loan × rate × years) ÷ months. It is exactly the top of the EMI bracket, so it is always too high.
  • The loan ÷ months offered as the EMI, as if there were no interest at all. It is the bottom of the bracket.
  • The total paid given for the interest. Take the loan away.
  • The yearly rate charged every month: in the first instalment, the loan × the yearly rate, twelve times too big.
  • For borrowing, the payment × months offered as the loan. It ignores that later payments are worth less today.

How to practise

  • Use “Kinds of question” to drill the EMI on its own until the bracket is automatic; every other kind starts from it.
  • Switch Answer by to “Typing the answer”: an EMI counts within 1%, totals within 1 of your currency, so you must finish the arithmetic.
  • Pick your own Currency; with ₹ the sums are in lakhs, as a real loan would be, and with the others in thousands.

Levels

It is untimed unless you turn the clock on. There is no last level: at least one dial turns without end. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

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