21 Concepts of Simple & Compound Interest | Complete SI & CI for Bank Exams 2026 | By Navneet Sir

Summary

The session provides a broad review of simple interest (SI) and compound interest (CI), progressing from basic definitions to exam-style calculations. The instructor emphasizes understanding how interest grows, choosing an efficient calculation method, and recognizing common wording in questions.

1. Core terms and simple interest

• Principal (P): The original amount invested or borrowed.
• Interest: The extra money earned or paid beyond the principal.

• Amount (A): Principal plus interest: A = P + interest

• Rate (R): The interest rate, usually stated per annum.

• Time (T): The duration of the investment or loan.

With simple interest, interest is calculated only on the original principal in each period.

• SI = P × R × T / 100
• Rate (%) = (one year’s SI / P) × 100

The instructor demonstrates several ways to solve SI questions: using the formula, calculating interest period by period, or combining the rate across years. For example, a constant annual rate of 8% gives 24% total simple interest over three years.

2. Common SI question types and methods

• Finding the principal: Rearrange the SI formula, or first determine what percentage of the principal the given interest represents.
• Finding the amount: Calculate SI, then add it to the principal. Alternatively, add the total SI percentage to 100% and apply that percentage to the principal.
• Finding the rate: Work out the interest for one year, then compare it with the principal.
• “Doubles itself” or “becomes triple” wording: These phrases describe the final amount. If an amount doubles, the interest equals the original principal; if it triples, the interest is twice the principal.
• Difference in SI over two durations: With the same principal and rate, the difference between the interest for, say, five years and three years is the SI earned during the two-year gap. This can be used to find the principal or rate.
• Amounts at different times: When the same principal amounts to different values after different numbers of years, the difference between the amounts is the SI for the difference in time. To recover the principal from an amount, subtract the SI for the same time period as that amount.
• Changing annual SI rates: Add the interest percentages for the relevant years, then apply the combined percentage to the principal.
• Money split between investments at different rates: Do not simply add the rates or assume the portions are equal. Represent the unknown portion, calculate the interest from each investment, and equate their total to the stated interest. The instructor also demonstrates an alligation or weighted-average approach.

3. Compound interest: definition and calculation

Under compound interest, each period’s interest is calculated on both the original principal and the interest accumulated in earlier periods. Thus, previously earned interest also earns interest.

• Amount after n periods: A = P(1 + R/100)ⁿ

• CI = A − P

The instructor presents several ways to solve CI questions:

• Slab or tree method: Track the interest earned on the principal and the additional interest earned on prior interest. For two years, for example, the second year’s interest includes interest on the first year’s accrued interest.
• Multiplier or chain method: For each period, multiply by the growth factor (1 + R/100). Apply the factor once per period, then subtract the principal from the final amount if the question asks for CI.
• Ratio method: Express the principal-to-amount ratio for each period, then combine the ratios to find the overall amount or interest ratio.
• Effective-rate method: Combine successive rates rather than treating them as simple additions.

For two successive rates a% and b%, the combined CI rate is:

a + b + ab/100

For three years, the instructor combines rates sequentially. For example, a constant rate of 10% over three years gives a total growth rate of 33.1%, not 30%.

4. CI and SI comparisons

The instructor presents shortcuts for finding the difference between compound and simple interest:

• For two years: CI − SI = P × R² / 100²

• For three years: CI − SI = [P × R² × (300 + R)] / 100³

These shortcuts apply only to the specified time periods. For other durations, calculate SI and CI separately or use an appropriate method.

5. Growth problems and compounding frequency

• Doubling or multiplying under CI: Express the starting and final amounts as powers of the same base. If the amount doubles in eight years, for instance, reaching eight times the principal takes 24 years under the same compounding conditions, because 8 is (2^3).
• Half-yearly compounding: Halve the annual rate and double the number of periods.
• Quarterly compounding: Divide the annual rate by four and multiply the number of periods by four.
• Population growth: Treat the starting population as the principal and the later population as the amount. Apply the CI growth multiplier for the stated years.
• Different CI rates in different years: Apply each year’s growth factor in sequence—for example, multiply by (1 + R_1/100), then (1 + R_2/100), and so on.

6. General exam advice

The instructor repeatedly advises students to understand the underlying concept rather than memorize a single procedure. The same question may be solved using a formula, a period-by-period layout, ratios, or effective rates; students should choose the method that is quickest and least error-prone.

The instructor also highlights that words such as “amounts to,” “becomes,” and “doubles itself” often indicate the final amount, while “amount of” may refer to the principal in some question constructions. Students should check the wording and time period carefully.

Speakers and sources featured

• Main speaker: One male mathematics instructor. The subtitles identify him inconsistently as “Tiwari” at the opening and refer to “Navneet Sir” elsewhere; the transcript does not clearly resolve the discrepancy.
• Audience: The instructor addresses students and prompts them to respond, but no distinct student speaker is identifiable in the subtitles.
• Sources and resources mentioned: Viral Maths and its maths playlists; the instructor’s Telegram group for session PDFs; Viral Happiness Foundation, which the instructor says receives the channel’s YouTube revenue; and promotional mentions of the instructor’s books and learning materials.