Math Case Study for Class 8 Compound Interest

Math Case Study for Class 8 Compound Interest Online Practice Test

Math Case Study for Class 8 Compound Interest Online Practice Test

The Math Case Study for Class 8 Compound Interest Online Practice Test introduces students to real-world situations that involve growth, interest, and long-term calculations. It helps them apply CI formulas correctly while developing confidence. Moreover, the test format encourages careful reading and accurate computation.

Understanding Compound Interest Concepts

This section explains principal, rate, and compounding in simple language. Students learn how values change over time. Additionally, stepwise examples make each concept easier to understand. These explanations support revision and strengthen learning.

Applying Concepts Through Online Practice

The online test presents relatable CI problems. Each question encourages logical reasoning and steady calculation. Furthermore, structured practice improves exam preparation. Students gain clarity through repeated application, making learning more effective and engaging.

Case Study 2: Simple and Compound Interest – Advanced

After consulting with a financial advisor, **Riya** refined her savings plan to accommodate short-term educational expenses and smaller periodic withdrawals. She considers three practical situations: short-term emergency savings, medium-term goal funding, and a loan repayment scenario for a small equipment purchase. To model these, she opens accounts with different banks that offer a mix of **simple interest (SI)** schemes and **compound interest (CI)** schemes with different compounding frequencies (annual and half-yearly). Riya records deposits of amounts such as Rs. 3000, Rs. 4500 and Rs. 8000 over periods ranging from 2 to 4 years at various nominal rates (including non-integer rates like 7.5%). She also examines the effect of compounding frequency by comparing annual and half-yearly compounding for the same nominal annual rate. Riya wants to (a) compute exact maturity amounts, (b) approximate gains due to higher compounding frequency, (c) determine implied principal when maturity and rate are known, and (d) decide which scheme gives higher effective returns for her medium-term needs. Use Riya’s recorded cases below to answer the questions, showing all steps and proper rounding to two decimal places when necessary.

1. Riya deposits Rs. 4500 at 7.5% per annum under a simple interest scheme for 4 years. What is the total simple interest earned at the end of 4 years?

Solution:
Using the simple interest formula: $SI=\frac{P\times R\times T}{100}$
Substitute $P=4500$, $R=7.5$, $T=4$:
$SI=\frac{4500\times 7.5\times 4}{100}=\frac{4500\times 30}{100} = 1350$
Thus the interest earned is Rs. **1350.00**.
Correct answer is option **(a)**.

2. Riya places Rs. 8000 for 2 years at a nominal rate of 10% per annum. Bank X compounds annually while Bank Y compounds half-yearly. Approximately how much more (to two decimal places) will she get from Bank Y than from Bank X after 2 years?

Solution:
**Bank X (Annual Compounding):**
$A_X=8000(1.10)^2=8000\times 1.21=9680.00$
**Bank Y (Half-Yearly Compounding, $R/2 = 5\%$, $n=4$ periods):**
$A_Y=8000(1.05)^4 = 8000 \times 1.21550625 \approx 9724.05$
**Difference:** $9724.05 – 9680.00 = 44.05$
Correct answer is option **(a)**.

3. A certain amount invested at compound interest compounded annually at 10% per annum becomes Rs. 12,100 after 2 years. What was the principal?

Solution:
Compound Amount $A=P(1+\tfrac{R}{100})^T$. Solving for $P$:
$P=\frac{A}{(1+\tfrac{R}{100})^T}=\frac{12100}{(1.10)^2}=\frac{12100}{1.21}=10000$
Hence principal is Rs. **10,000**.
Correct answer is option **(a)**.

4. A borrower takes a loan which under simple interest doubles in 8 years. What is the annual simple interest rate (in %) on the loan?

Solution:
If the amount doubles, the Simple Interest ($SI$) equals the Principal ($P$).
$SI = P \Rightarrow \frac{P\times R\times T}{100}=P$
$\frac{R\times T}{100}=1$
$R=\frac{100}{T}=\frac{100}{8}=12.5\%$.
Correct answer is option **(b)**.

5. Riya compares two offers for a 3-year deposit of Rs. 3000. Bank A offers 9% per annum compounded annually. Bank B offers 8% per annum under simple interest. After 3 years, how much more (to two decimal places) does Bank A pay compared to Bank B?

Solution:
**Bank A (CI annually, 9%):**
$A_A=3000(1.09)^3 = 3000 \times 1.295029 \approx 3885.09$
**Bank B (SI, 8%):**
$SI_B=\frac{3000\times 8\times 3}{100}=720$
$A_B=3000+720=3720.00$
**Difference:** $3885.09 – 3720.00 = 165.09$
Correct answer is option **(b)**.

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