Exercise 5.3 — Simple and Compound Interest
Simple Interest and Compound Interest problems.
Exercise 5.3 – Simple Interest, Compound Interest & Depreciation
Exercise 5.3 of Class 8 Mathematics (CBSE, Telangana & Andhra Pradesh syllabus) introduces two of the most practical concepts in everyday finance: Simple Interest (S.I.) and Compound Interest (C.I.). You'll also learn about depreciation — how the value of items like TVs, cars, and machinery reduces over time — and how to apply compound interest formulas to real situations like loans, population growth, and bacteria growth.
The most important skill in this exercise is recognizing which formula to use. Simple interest is calculated on the same principal every time, while compound interest is calculated on a principal that keeps changing (growing or shrinking) after each time period. Most questions in this exercise are direct applications of one of the four core formulas below.
Key Formulas You Must Know
| Concept | Formula | Used In |
|---|---|---|
| Simple Interest | I = (P × T × R) / 100 | Q1, Q5, Q9, Q11, Q12 |
| Amount (Simple Interest) | A = P × (100 + TR) / 100 | Q1, Q5, Q9 |
| Amount (Compound Interest) | A = P × (100 + R)n / 100n | Q3, Q4, Q6, Q8–Q15 |
| Compound Interest | I = A − P | Q3, Q4, Q7, Q9, Q12, Q15 |
| Value After Depreciation | A = P × (100 − R)n / 100n | Q2, Q13 |
| Compounding Period (n) | Annually: n = T; Half-yearly: n = 2T, R = R/2; Quarterly: n = 4T, R = R/4 | Q8, Q15 |
Sudhakar borrows ₹15,000 at 9% per annum simple interest for 8 years. We first find the total amount he must repay, then divide it equally over all the monthly instalments for 8 years.
| Symbol | Meaning | Value |
|---|---|---|
| P | Principal | ₹15,000 |
| R | Rate of interest | 9% p.a. |
| T | Time | 8 years |
Step 1: Total Amount to Repay
Step 2: Monthly Repayment
A TV bought for ₹21,000 depreciates (loses value) by 5% after 1 year. Depreciation works exactly like compound interest, except the value decreases instead of increasing — so we use (100 − R) instead of (100 + R).
Value after depreciation = Original Price × (100 − R%) / 100
A sum of ₹8000 is invested at 5% per annum for 2 years, compounded annually. This is the most direct application of the compound interest formula — apply (100 + R)/100 twice (raised to the power n = 2).
A = P × [(100 + R)/100]n
A sum of ₹6500 earns 5% in the first year and 6% in the second year, compounded annually. Since the rates differ each year, we cannot use the formula with a single power n — instead, we calculate the amount for the first year, then use that result as the new principal for the second year.
Step 1: First Year (Rate = 5%)
Step 2: Second Year (Rate = 6%, P = ₹6825)
Prathibha borrows ₹47,000 at 17% simple interest for 5 years. This question follows the exact same two-step pattern as Question 1: first find the total repayable amount, then divide it across the monthly instalments.
(a) Total Amount After 5 Years
(b) Monthly Repayment
The population of Hyderabad was 68,09,000 in 2011, growing at 4.7% per year. We need the population at the end of 2015 — that is, after 4 years. Population growth, like compound interest, multiplies by the same growth factor every year, so we apply the compound interest formula with n = 4.
A sum of ₹10,000 is invested at 8½% per annum compounded annually for 1 year and 3 months. When the time period includes a fraction of a year, the compounding formula is applied for the whole year(s) first, and then simple interest is applied for the remaining months on the new principal.
Step 1: Compound Interest for 1 Full Year
Step 2: Simple Interest for Remaining 3 Months (= ¼ year)
Arif takes a loan of ₹80,000 at 10% per annum for 1½ years. We find the final amount under two different compounding methods — annual and half-yearly — and compare the difference. The key change for half-yearly compounding: the rate is halved and the number of periods is doubled.
Method 1: Compounded Annually
Method 2: Compounded Half-Yearly
Difference Between the Two Methods
A sum of ₹12,000 is borrowed at 6% per annum for 2 years. We compare the total amount payable under simple interest versus compound interest (compounded annually), and find the extra amount due to compounding.
Simple Interest Amount
Compound Interest Amount
Extra Amount Due to Compounding
A bacteria culture starts at 5,06,000 and grows at 2.5% per hour. We find the count after 2 hours. Since the growth compounds every hour, n = 2 — the exact same structure as the population growth in Question 6, just with a smaller initial value and a shorter time unit (hours instead of years).
Kamala borrows ₹26,400 at 15% per annum compounded yearly, and needs to repay it after 2 years and 4 months. Just like Question 7, we apply compound interest for the whole years first, then simple interest for the extra months on the new amount.
Step 1: Compound Interest for First 2 Years
Step 2: Simple Interest for Next 4 Months (= 1/3 year)
Bharathi borrows ₹12,500 at 12% simple interest for 3 years, while Madhuri borrows the same amount at 10% compound interest for the same period. We need to find who pays more interest, even though their rates and methods are completely different.
Bharathi's Interest (Simple Interest at 12%)
Madhuri's Interest (Compound Interest at 10%)
Comparison
Machinery worth ₹10,000 depreciates by 5%. We find its value after 1 year — this is the same depreciation formula used in Question 2, applied to a different item and value.
A city's current population is 12 lakh (12,00,000), growing at 4% per year. We find the population after 2 years using the same compound growth formula seen in Questions 6 and 10, here with whole numbers that simplify nicely.
A sum of ₹1000 is invested for 1 year at 10% per annum, but the interest is compounded quarterly (every 3 months). When compounding quarterly, the annual rate is divided by 4 and the number of periods n becomes 4 (for 1 year).
Quarterly compounding: Rquarter = R ÷ 4, n = T × 4
Common Mistakes to Avoid in Exercise 5.3
- Confusing simple interest and compound interest formulas: Simple interest uses (100 + TR)/100 with the original principal throughout. Compound interest uses [(100 + R)/100]n, where the principal effectively grows every period.
- Getting the compounding frequency wrong: For half-yearly compounding, halve the rate and double the number of periods. For quarterly compounding, divide the rate by 4 and multiply the number of periods by 4.
- Mishandling fractional time periods: When time includes extra months (like 1 year 3 months or 2 years 4 months), apply compound interest for the full years first, then simple interest for the remaining months on the new amount — not the original principal.
- Using (100 + R) for depreciation: Depreciation reduces value, so always use (100 − R), not (100 + R). This is the most common sign error in this exercise.
- Forgetting to subtract P at the end: Many questions ask for the interest, not the amount. Always check whether the answer required is A or (A − P).
What Exercise 5.3 Prepares You For
Simple and compound interest are foundational for understanding exponential growth and decay, a theme that reappears throughout higher mathematics. The percentage techniques practised in Exercise 5.2 on profit, loss, discount, and GST combine directly with the compounding ideas here to solve more advanced financial mathematics problems.
The exponent-based formulas — (100 + R)n — also connect to Exponents and Powers, since compound interest is really just repeated multiplication expressed using powers. In Class 9 and Class 10, similar growth and decay models appear in Direct and Inverse Proportions and various real-world application problems.