Math Case Study for Class 8 Simple and Compound Interest

Math Case Study for Class 8 Simple and Compound Interest Online Test

Math Case Study for Class 8 Simple & Compound Interest Online Test

The Math Case Study for Class 8 Simple & Compound Interest Online Test helps students understand both SI and CI concepts through practical examples. It introduces real-life situations that require careful application of formulas. Moreover, short examples guide students step by step.

Learning SI and CI Through Mixed Questions

This section explains how Simple Interest and Compound Interest differ. Students explore various situations that compare growth over time. Additionally, easy-to-follow visuals help simplify each calculation.

Practice and Application for Better Understanding

The online test includes mixed-interest problems that strengthen logical reasoning. Each question encourages clear thinking and accuracy. Furthermore, structured practice boosts exam readiness and builds confidence effectively.

Case Study 3: Simple and Compound Interest – Practical Application

**Riya** is helping her school start a small community library and needs to manage a fund for book purchases and maintenance. She decides to use short-term fixed deposits and small savings accounts to keep the corpus growing while keeping some liquidity for occasional purchases. To test realistic scenarios, she considers different combinations of principal amounts, interest rates, and compounding frequencies. She records a set of experiments: (1) a moderate sum placed for three years in an account that compounds **quarterly**, (2) a larger sum placed for five years where she compares **simple interest (SI) against compound interest (CI)**, (3) a case where the maturity amount and principal are known and she needs to infer the **effective annual rate**, (4) a quick planning question about how long it will take to **double the corpus** under a given compound rate, and (5) a loan-like arrangement where the library borrows small equipment funds at simple interest and repays after a fixed period. Riya must perform accurate calculations, compare effective returns, and interpret the results to make practical decisions about which schemes give adequate growth without jeopardizing liquidity. The following five MCQs are based strictly on these recorded experiments.

1. Riya places Rs. 3000 in an account that compounds quarterly at an annual nominal rate of 6% for 3 years. What is the amount at maturity (rounded to two decimal places)?

Solution:
Quarterly rate $r = \frac{6\%}{4} = 1.5\% = 0.015$. Number of periods $n = 3 \times 4 = 12$.
$A = P(1+r)^n = 3000(1.015)^{12}$
$A \approx 3000\times 1.1956185 \approx 3586.85$
Correct answer is option **(b)**.

2. Riya compares Rs. 5000 invested for 5 years at 9% per annum under simple interest and compound interest (compounded annually). How much greater (approximately) is the compound interest maturity amount than the simple interest maturity amount? (Round to two decimal places.)

Solution:
**Simple Interest (SI):** $SI = \frac{5000\times 9\times 5}{100}=2250$. $A_{SI}=5000+2250=7250.00$.
**Compound Interest (CI):** $A_{CI}=5000(1.09)^5 \approx 5000\times 1.5386239 \approx 7693.12$.
**Difference:** $7693.12 – 7250.00 = 443.12$.
Correct answer is option **(b)**.

3. An investment of Rs. 8000 becomes Rs. 10,368 after 3 years with annual compounding. What is the approximate annual interest rate (to two decimal places)?

Solution:
Use $A=P(1+\tfrac{R}{100})^T$. $\left(1+\frac{R}{100}\right)^3 = \frac{10368}{8000} = 1.296$.
$1+\frac{R}{100} = 1.296^{1/3} \approx 1.0902724$
$R \approx 0.0902724\times 100 \approx 9.03\%$.
Correct answer is option **(b)**.

4. Riya wants the library corpus to double under compound interest compounded annually at a rate of 12% per annum. Approximately how many years will it take to double?

Solution:
We solve for $t$: $(1+0.12)^t=2$.
Using logarithms: $t=\frac{\ln 2}{\ln 1.12}\approx \frac{0.6931}{0.1133} \approx 6.1163$.
Thus approximately **6.12 years** (Rule of 72 gives $\approx 72/12 = 6$ years, which is close).
Correct answer is option **(a)**.

5. The library borrowed Rs. 7500 for equipment and repaid Rs. 9750 after 3 years under simple interest. What was the annual rate of interest charged?

Solution:
Total interest paid $SI = 9750 – 7500 = 2250$.
Using $SI=\frac{P\times R\times T}{100}$: $2250=\frac{7500\times R \times 3}{100}$.
$R=\frac{2250\times 100}{7500\times 3}=\frac{225000}{22500}=10\%$.
Correct answer is option **(b)**.

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