7. Simple interest and compound interest
Free study material · concepts, shortcuts & solved questions
Simple interest is linear: SI=PRT/100 and amount=P+SI. Compound interest reinvests interest: A=P(1+r/100)^n and CI=A−P. For half-yearly compounding, use r/2 per half-year and 2n periods. For two years, CI−SI=P(r/100)^2.
Method before formula Keep rate and time compatible. A rate per annum requires time in years. For changing rates, compound each period with its own multiplier rather than averaging rates. |
Formula and decision table
Example | Calculation |
SI | P=5000,R=8%,T=2: SI=800 |
CI | P=10000,R=10%,2 years: A=12100, CI=2100 |
Half-yearly | 10% p.a. becomes 5% per half-year |
Worked understanding
A reliable solution has five visible moves: identify the data, choose the base or unit, write the rule, substitute carefully, and check the size of the answer. The examples in this chapter are deliberately small so that the method remains visible.
Calculation discipline Before pressing ahead, state the denominator or unit in words. For example: profit on CP, discount on MP, average over number of items, speed in metres per second, and probability over the fixed sample space. |
Solved examples from this chapter
Question focus | Correct move | Answer |
SI on 5000 at 8% for 2 years: | 5000×8×2/100=800. | B. 800 |
CI on 10000 at 10% for 2 years: | Amount=12100, so CI=2100. | B. 2100 |
For half-yearly compounding, rate per period is: | There are two periods per year. | C. r/2 |
What an examiner is testing
The options around Simple interest and compound interest usually represent a wrong base, a missed conversion, a sign error or a shortcut used outside its condition. Say the base and unit before calculating, estimate the result, and use substitution or a reverse operation as the final check.
Step-by-step answer construction
Example 1: SI on 5000 at 8% for 2 years: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 800, because 5000×8×2/100=800.
Example 2: CI on 10000 at 10% for 2 years: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 2100, because Amount=12100, so CI=2100.
Example 3: For half-yearly compounding, rate per period is: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is r/2, because There are two periods per year.
Chapter practice
1. SI on 5000 at 8% for 2 years:
(A) 400 (B) 800 (C) 900 (D) 1000
Answer: B. 800 | Explanation: 5000×8×2/100=800.
2. CI on 10000 at 10% for 2 years:
(A) 2000 (B) 2100 (C) 2200 (D) 2400
Answer: B. 2100 | Explanation: Amount=12100, so CI=2100.
3. For half-yearly compounding, rate per period is:
(A) r (B) 2r (C) r/2 (D) r²
Answer: C. r/2 | Explanation: There are two periods per year.
SSC CGL speed and trap clinic
For Simple interest and compound interest, speed comes after classification. Before calculating, say aloud what the number means, what the denominator is, and what unit the answer must carry. Then use the nearest-option check to catch a sign, base or conversion error.
Checkpoint | What to verify | Typical SSC mistake |
Base | Which quantity is the base in Simple interest and compound interest? | Using selling price instead of cost price, or part instead of total |
Unit | Are time, distance, area and rate in compatible units? | Mixing hours with minutes or km/h with m/s |
Direction | Should the answer increase, decrease or stay bounded? | Accepting an impossible negative length or probability above 1 |
Estimate | What range should the answer lie in before exact work? | Trusting a long calculation that is far from the options |
Reverse check | Can the answer be substituted back into the condition? | Stopping at an algebraic value without verification |
Mini decision drill
1. Write the first operation you would perform in a Simple interest and compound interest question and why.
2. State the most dangerous denominator or unit in this chapter.
3. Give one condition under which a shortcut would be invalid.
4. Create a small numerical example and verify it by a second method.
Revision evidence Do not tick this chapter because you recognised the formula. Tick it only after you solve one direct question, one altered-condition question and one mixed-paper question correctly. |