Class 10 Mathematics | Unit 2 Compound Interest Formula & Key Points
Introduction to the Chapter
Welcome to the essential guide for Unit 2 Compound Interest (चक्रीय ब्याज) in the Class 10 Compulsory Mathematics curriculum. This unit falls under the Arithmetic (अङ्कगणित) section.
Understanding the difference between Simple Interest and Compound Interest is vital for the SEE examination. This page summarizes the key formulas for calculating Compound Amount (CA) and Compound Interest (CI) under various conditions such as annual compounding, semi-annual compounding, and fractional time periods.
संकेतहरू (Notations):
- $T =$ वर्षको सङ्ख्या (Number of years)
- $R =$ वार्षिक व्याजदर (Rate of interest)
- $P =$ सावाँ (Principal)
1. ब्याज चक्रीय वार्षिक हुँदा (Annual Compounding)
| अवस्था (Condition) | सूत्र (Formulae) |
|---|---|
|
समय $T$ (पूर्णसङ्ख्या) हुँदा When Time $T$ is a whole number |
CA: $P\left(1+\frac{R}{100}\right)^T$
CI: $P\left[\left(1+\frac{R}{100}\right)^T – 1\right]$
|
|
$T$ वर्ष र $M$ महिनामा In $T$ years and $M$ months |
CA: $P\left(1+\frac{R}{100}\right)^T \left(1+\frac{MR}{1200}\right)$
CI: $P\left[\left(1+\frac{R}{100}\right)^T \left(1+\frac{MR}{1200}\right) – 1\right]$
Note: If T is a fraction, convert to years & months. For $\le 1$ year, CI = SI.
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2. ब्याज चक्रीय अर्धवार्षिक हुँदा (Semi-Annual Compounding)
| अवस्था (Condition) | सूत्र (Formulae) |
|---|---|
|
$2T$ (पूर्णसङ्ख्या) हुँदा When $2T$ is a whole number |
CA: $P\left(1+\frac{R}{200}\right)^{2T}$
CI: $P\left[\left(1+\frac{R}{200}\right)^{2T} – 1\right]$
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|
$2T$ को मान वर्ष र महिनामा If $2T$ involves years & months |
CA: $P\left(1+\frac{R}{200}\right)^{2T} \left(1+\frac{MR}{1200}\right)$
CI: $P\left[\left(1+\frac{R}{200}\right)^{2T} \left(1+\frac{MR}{1200}\right) – 1\right]$
Note: For $\le 6$ months, Semi-Annual CI = Simple Interest.
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3. हरेक वर्षको व्याजदर फरक-फरक हुँदा (Variable Interest Rates)
If $R_1$ is the rate for $T_1$ years and $R_2$ is the rate for $T_2$ years:
चक्रीय मिश्रधन (Compound Amount):
$$CA = P\left(1+\frac{R_1}{100}\right)^{T_1} \left(1+\frac{R_2}{100}\right)^{T_2}$$चक्रीय ब्याज (Compound Interest):
$$CI = P\left[\left(1+\frac{R_1}{100}\right)^{T_1} \left(1+\frac{R_2}{100}\right)^{T_2} – 1\right]$$4. अन्य महत्वपूर्ण सूत्रहरू (Other Important Formulae)
A. From Consecutive Amounts ($CA_1, CA_2$)
If $CA_1$ is for $T$ years and $CA_2$ is for $T+1$ years:
Rate (R): $R = \left(\frac{CA_2}{CA_1} – 1\right) \times 100\%$
Principal (P): $P = \frac{CA_1}{\left(1+\frac{R}{100}\right)^T}$
B. From Consecutive Interests ($CI_1, CI_2$)
If $CI_1$ is for 1 year and $CI_2$ is for 2 years:
Rate (R): $R = \left(\frac{CI_2}{CI_1} – 2\right) \times 100\%$
Principal (P): $P = \frac{CI_1 \times 100}{R}$
C. CI र SI को सम्बन्ध (Relation between CI and SI)
Full Chapter PDF Manual
For offline study, access the complete PDF manual below.
Disclaimer
This pdf notes is based on old course but same as most of the question in new course and taken from manual written by:
- Title: Compulsory Maths SEE Manual
- Writer: Dr Simkhada
- Publisher: Readmore Publishers & Distributors
- Edition: 2076
Additional References
For further reading on the mathematics curriculum in Nepal including this chapter, please visit the Ministry of Education, Science and Technology. You can also explore general financial mathematics on Wikipedia.