Simple & Compound Interest in One Shot 🔥 No Formulas, Just Logic | CAT 2026

Summary

The instructor teaches simple interest (SI), compound interest (CI), and loan-installment problems through percentage reasoning rather than memorized formulas. The central idea is to track how the balance changes over time: multiply by a growth factor when interest is added, subtract withdrawals or payments when they occur, and compare balances to find interest for a particular period.

1. Basic terms and percentage factors

• Principal (P): The initial amount invested or borrowed.
• Rate: The percentage charged or earned per year, or per other stated period.
• Time: The number of periods the amount earns interest or accrues charges.
• Amount: The principal plus interest—the full balance at the end.

To apply a percentage as a multiplier, add it to 1. For example, a 10% increase means multiplying by 1.10. To find just the increase, use 0.10.

The instructor recommends reviewing profit-and-loss concepts first, since converting percentages into multipliers is important throughout the lesson.

2. Simple interest

With SI, interest is calculated on the original principal each period, so the increase is the same each year.

• At a 10% annual rate, the balance increases by 10% of the original principal each year.
• To find the total after several years, add the same yearly increase repeatedly.
• To find the interest, subtract the original principal from the final amount.
• To find the interest earned in a particular year, compare that year’s balance with the previous year’s balance. Under SI, the increase is constant.

The instructor uses a 13.5% rate to illustrate converting a percentage into an amount multiplier. Some of the transcript’s later arithmetic in this example is garbled, but the underlying lesson is that SI adds a fixed amount based on the original principal.

3. Compound interest

With CI, each period’s interest is added to the balance, and later interest is calculated on the new balance.

• At 10% per year, multiply the balance by 1.10 each year.
• For two years, apply the multiplier twice; for three years, apply it three times.
• The final balance is the amount. Subtract the original principal to find total compound interest.
• Unlike SI, the base grows over time.

The instructor’s shorthand is to apply the rate multiplier repeatedly rather than memorize a compound-interest formula.

4. Compounding more often than annually

When interest is compounded more frequently, adjust both the rate per period and the number of periods:

• Half-yearly: Use half the annual rate and apply it twice per year.
• Quarterly: Use one-quarter of the annual rate and apply it four times per year.
• Apply the adjusted multiplier once for each compounding period in the full term.

For example, with a 12% annual rate compounded quarterly, each quarter uses a 3% rate, so the balance is multiplied by 1.03 four times over a year.

5. Finding interest in a particular year

To find the interest earned during one year under CI, subtract the balance at the start of that year from the balance at the end of it.

• Interest in year 8 = balance after 8 years minus balance after 7 years.
• Interest in year 5 = balance after 5 years minus balance after 4 years.

The instructor contrasts this with SI, where the yearly interest is the same each year.

6. Loans, equal installments, and future value

The lesson treats repayment questions as balance-tracking problems. The key is to account for when each installment is paid:

• Start with the loan and let it grow by the interest multiplier for the relevant periods.
• If an installment is paid at the end of a year, it stops accruing interest after that payment.
• To compare all payments with the original loan at a common date, grow each payment forward for the remaining years.
• Alternatively, work backward by discounting later payments to the starting date.
• For equal installments, represent each installment with the same unknown, such as x, and account for the different number of periods each one earns or avoids interest.
• If installments change by a fixed amount, express them accordingly—for example, the first as x, the second as x plus the increase, and the third as x plus twice the increase.

If the principal is unknown but the installments are given, the same relationship can be rearranged to find the principal. The transcript’s detailed arithmetic for some installment examples is inconsistent or garbled, so the reliable takeaway is the timing method, not the spoken numerical results.

7. Types of questions demonstrated

The practice section covers several applications:

• Deposits and withdrawals: Grow the account balance for each period, subtract withdrawals when they occur, and then continue compounding.
• Comparing SI and CI: Calculate the interest earned in specific years and compare the differences. In one example, the instructor initially makes an algebraic sign error, corrects it, and obtains a 10% rate.
• Inferring a rate and principal: Compare balances at different times, then use the growth factor to recover the initial investment.
• Finding principal from the SI–CI difference: Compare the total interest under both methods and use the difference to determine the starting amount.
• Equal loan repayments: Account for each installment’s timing and solve for either the loan amount or the installment.

Main lesson

The instructor’s overall method is to avoid memorizing a collection of formulas and instead:

1. Convert each percentage into a multiplier.
2. Apply that multiplier once per interest period.
3. Track payments, withdrawals, or deposits when they occur.
4. Compare balances to isolate interest for a particular period.
5. Set up an equation when an amount or installment is unknown.

The instructor presents the session as CAT-focused preparation and says it builds on earlier profit-and-loss material. Several exact figures in the auto-generated subtitles appear mistranscribed, so the general methods are clearer than some of the recorded calculations.

Speakers and sources

• Instructor/presenter: One unnamed speaker teaches throughout the video. The presenter describes themself as a student.
• ChatGPT: The presenter says the final loan/EMI practice question was created with ChatGPT.
• Other references, not additional speakers: The presenter mentions an earlier profit-and-loss video and refers to CAT, IMS SIMCAT, and “DSCAT” questions or question styles. No other teacher or interviewee is heard in the subtitles.