Simple and Compound Interest Module Review

Lesson 14 of 1814 minPDF notesFree

Simple and Compound Interest Module Review

Use this review after the Simple Interest lesson and Compound Interest and Growth Comparisons. It contains 18 fresh, mixed questions: six revisit SI skills, ten use CI or its growth/reverse applications, and two compare the models. The order is mixed so that you must choose the model before choosing a formula.

This review samples the covered skills; it does not reassess every SI variation. The earlier SI practice also covers general unknown time and monthly-rate questions. Day-count conventions are not tested here. These are original learning questions, not official past questions or a full RRB CBT mock. There is no question-frequency or selection prediction.

How to attempt

Work without a time limit. Select one answer A–D for each question. Scoring is +1 correct, 0 incorrect or unattempted, with no negative marking and no pass cutoff. A score is a record of this practice attempt, not a prediction of exam performance. Attempt all questions before reading the answers.

Write a short setup beside each calculation:

What is asked: principal, amount, interest, rate, time or model?
Does interest stay on the original principal, or is the base updated each period?
What is the rate per period, and how many full periods are there?
For an annual quote divided into half-years or quarters, has the question explicitly given the nominal-rate convention?

Unless a question says otherwise, the stated interest model has no extra deposits, withdrawals, repayments, fees or taxes. All growth/depreciation quantities are hypothetical models. Calculate exactly; all required numerical answers here have exact terminating values.

Recall before you begin

Without opening a formula list, explain why one annual period gives the same SI and CI at the same rate, why later periods can differ, and why a rate already stated per quarter must not be divided by four. If you cannot yet explain a step, use the relevant lesson before attempting the mixed review.

Questions

1. Find the amount on ₹7,200 at 5% per year simple interest for eight months.

A. ₹240 B. ₹7,560 C. ₹7,440 D. ₹10,080

2. Find the amount on ₹4,800 after two full years at 5% per year, compounded annually.

A. ₹5,292 B. ₹5,280 C. ₹492 D. ₹5,040

3. ₹8,400 becomes ₹9,660 after 2.5 years under simple interest at a fixed annual rate. Find that annual rate.

A. 15% B. 46% C. 7.5% D. 6%

4. Find CI on ₹18,000 for one year at a nominal annual 10%, compounded half-yearly. The annual quote is divided equally between two half-years.

A. ₹1,800 B. ₹1,845 C. ₹19,845 D. ₹900

5. A hypothetical quantity starts at 6,250 and increases by 20% of its current size at each of two annual model steps. Find the final quantity.

A. 9,000 B. 8,750 C. 2,750 D. 7,500

6. With unchanged principal and fixed simple-interest rate, an amount is ₹5,750 after two years and ₹6,875 after five years. Find the original principal.

A. ₹5,750 B. ₹4,625 C. ₹5,000 D. ₹5,300

7. The amount is ₹9,075 after two full years at 10% per year, compounded annually. Find the original principal.

A. ₹7,169.25 B. ₹7,500 C. ₹8,250 D. ₹9,075

8. ₹9,000 earns simple interest at 4% per year for two years, then 7% per year for one year, always on the original principal. Find total interest.

A. ₹720 B. ₹990 C. ₹10,350 D. ₹1,350

9. Find only the second year’s interest on ₹10,000 at 6% per year, compounded annually.

A. ₹636 B. ₹600 C. ₹1,236 D. ₹11,236

10. A hypothetical value of ₹50,000 loses 10% of its current value at each year-end for two years. Find its remaining value.

A. ₹40,000 B. ₹9,500 C. ₹40,500 D. ₹60,500

11. Which principal earns ₹1,170 simple interest at 6.5% per year in three years?

A. ₹18,000 B. ₹6,000 C. ₹7,170 D. ₹600

12. Find the amount on ₹16,000 for six months at a nominal annual 16%, compounded quarterly. Divide the nominal annual quote equally among four quarters.

A. ₹17,280 B. ₹16,640 C. ₹1,305.60 D. ₹17,305.60

13. ₹10,000 becomes ₹12,656.25 in two annual compounding periods at a constant rate that is zero or positive. Find the annual percentage rate.

A. 12.5% B. 26.5625% C. 13.28125% D. 112.5%

14. A sum triples in 24 years at a fixed simple-interest rate. In how many years will it double at that same rate?

A. 16 years B. 24 years C. 12 years D. 48 years

15. The rate is 2% per half-year, compounded half-yearly. Find the percentage increase in amount over one whole year.

A. 4% B. 4.04% C. 2% D. 2.01%

16. ₹7,000 becomes ₹9,317 at 10% per year, compounded annually. The duration is a whole number of years. Find it.

A. 1 year B. 2 years C. 3.31 years D. 3 years

17. On the same ₹12,000 at a fixed 10% per year for exactly two years, find CI minus SI. CI is compounded annually.

A. ₹120 B. ₹2,400 C. ₹2,520 D. ₹372

18. A sum starts at ₹8,000, reaches ₹8,800 after one year and ₹9,680 after two years. The rate is fixed at 10% per year and there are no deposits, withdrawals, fees or repayments. Which description matches these amounts?

A. Simple interest; the second-year base is ₹8,000. B. Annual compound interest; the second-year base is ₹8,800. C. Both simple and annual compound interest, because the rate is fixed. D. Neither model, because the rate must have changed.

Explained answers

1. Answer C

Match the annual rate with years: T=8/12=2/3. SI=7200×0.05×2/3=₹240; amount=7200+240=₹7,440. Check: a full year earns ₹360, and eight months earns two-thirds of that.

Check every option:

A: ₹240 is interest only.
B: ₹7,560 uses a full year.
C: ₹7,440 correctly adds eight-month interest to principal.
D: ₹10,080 treats eight months as eight years.

2. Answer A

A=4800×1.05^2=₹5,292. Check: year-one interest ₹240 gives ₹5,040; year-two interest=5040×0.05=₹252, giving ₹5,292.

Check every option:

A: ₹5,292 uses the new base in year 2.
B: ₹5,280 is the corresponding SI amount.
C: ₹492 is total CI.
D: ₹5,040 stops after year 1.

3. Answer D

SI=9660−8400=₹1,260. R=1260×100/(8400×2.5)=6% per year. Check: annual interest ₹504; over 2.5 years it is ₹1,260.

Check every option:

A: 15% is total interest as a percentage of principal over 2.5 years.
B: 46% incorrectly uses the whole ₹9,660 as interest.
C: 7.5% uses two years instead of 2.5.
D: 6% reproduces the stated total amount.

4. Answer B

j=10/2=5% per half-year; N=2. A=18000×1.05^2=₹19,845; CI=₹1,845. Check: ₹900 interest in the first half and ₹945 in the second sum to ₹1,845.

Check every option:

A: ₹1,800 is the one-year annually compounded result or matching SI.
B: ₹1,845 includes both half-years with a changed base.
C: ₹19,845 is amount, not CI.
D: ₹900 is only first-half interest.

5. Answer A

Each factor is 1.20. Final quantity=6250×1.20^2=9,000. Check: 6250→7500→9000; the increases 1,250 and 1,500 are not equal.

Check every option:

A: 9,000 applies two current-base increases.
B: 8,750 adds 40% of the original quantity.
C: 2,750 is only the total increase.
D: 7,500 is the first-step result.

6. Answer C

The extra three years earn 6875−5750=₹1,125. Annual interest=1125/3=₹375. Subtract the first two years’ interest from ₹5,750: P=5750−2×375=₹5,000. Check: 5000+5×375=6875.

Check every option:

A: ₹5,750 already contains two years’ interest.
B: ₹4,625 subtracts the entire three-year difference from the two-year amount.
C: ₹5,000 reproduces both amounts.
D: ₹5,300 divides the difference by 5 rather than by the 3 extra years.

7. Answer B

P=9075/1.10^2=9075/1.21=₹7,500. Check forward: 7500→8250→9075. The full 21% increase is relative to the original principal, not the final amount.

Check every option:

A: ₹7,169.25 subtracts 21% of the final amount.
B: ₹7,500 reverses both annual multipliers.
C: ₹8,250 reverses one year only.
D: ₹9,075 is the final amount itself.

8. Answer D

SI=9000×(0.04×2+0.07×1)=₹1,350. Check: first stage ₹720; final stage ₹630; sum ₹1,350. Amount would be ₹10,350. Earlier interest is not added to the calculation base.

Check every option:

A: ₹720 omits the final year at 7%.
B: ₹990 counts only one year at 4% before the 7% year.
C: ₹10,350 is amount, not interest.
D: ₹1,350 adds the correctly weighted simple-interest periods.

9. Answer A

The year-two opening principal is 10000×1.06=₹10,600. Second-year interest=10600×0.06=₹636. Check: cumulative two-year CI is 600+636=₹1,236, which is not the quantity asked.

Check every option:

A: ₹636 uses the second-year opening amount.
B: ₹600 is only first-year interest.
C: ₹1,236 is cumulative interest over both years.
D: ₹11,236 is the amount after two years.

10. Answer C

The retained fraction each year is 0.90. Final value=50000×0.90^2=₹40,500. Check: 50000→45000→40500. The losses ₹5,000 and ₹4,500 total ₹9,500.

Check every option:

A: ₹40,000 subtracts 20% of the original value.
B: ₹9,500 is total depreciation.
C: ₹40,500 applies the decrease to the current value twice.
D: ₹60,500 uses two 10% increases.

11. Answer B

P=1170/(0.065×3)=1170/0.195=₹6,000. Check: annual interest=6000×0.065=₹390; three years earn ₹1,170.

Check every option:

A: ₹18,000 ignores the three-year duration.
B: ₹6,000 gives ₹390 per year.
C: ₹7,170 is the final amount for the correct principal.
D: ₹600 comes from using 0.65 for 6.5% instead of 0.065.

12. Answer D

j=16/4=4% per quarter; N=6/3=2. A=16000×1.04^2=₹17,305.60. Check: 16000→16640→17305.60; the second-quarter interest is ₹665.60.

Check every option:

A: ₹17,280 adds 8% of the original principal.
B: ₹16,640 stops after one quarter.
C: ₹1,305.60 is total CI.
D: ₹17,305.60 is the amount after both quarters.

13. Answer A

A/P=12656.25/10000=1.265625=(1.125)^2. Take the positive growth factor 1.125, then subtract 1: i=0.125, so the rate is 12.5%. Check: 10000→11250→12656.25.

Check every option:

A: 12.5% gives the required factor 1.125.
B: 26.5625% is the total two-year increase.
C: 13.28125% is half that total increase and assumes a fixed base.
D: 112.5% describes the yearly amount as a percentage of its opening base.

14. Answer C

Tripling the amount requires interest 2 P, while doubling requires interest P. At the same SI rate, interest is proportional to time, so doubling takes 24/2=12 years. Check: earning 2 P in 24 years means earning P in 12 years.

Check every option:

A: 16 scales total amounts in the ratio 2: 3 rather than the required interests 1: 2.
B: 24 is the tripling time.
C: 12 halves the required interest and the time.
D: 48 doubles the time even though less interest is needed.

15. Answer B

The rate is already per half-year, so use the factor 1.02 twice. One-year factor=1.02^2=1.0404. Percentage increase=(1.0404−1)×100=4.04%. Check using an arbitrary starting 100: 100→102→104.04.

Check every option:

A: 4% adds the two rates and omits interest on interest.
B: 4.04% is the full one-year increase.
C: 2% is only one half-year’s rate.
D: 2.01% divides the already per-half-year rate by 2, then compounds 1% twice.

16. Answer D

The annual factor is 1.10. The ledger 7000→7700→8470→9317 reaches the target after three years. Equivalently, 9317/7000=1.331=1.1^3. Check: every annual step uses the latest amount.

Check every option:

A: One year gives ₹7,700.
B: Two years gives ₹8,470.
C: 3.31 years divides the total increase ₹2,317 by fixed SI ₹700/year and also ignores the whole-year condition.
D: Three annual multipliers give ₹9,317.

17. Answer A

SI=12000×0.10×2=₹2,400. CI=12000×1.1^2−12000=₹2,520. Difference=₹120. Check with the two-year derivation: 12000×0.10^2=₹120.

Check every option:

A: ₹120 compares the matching two-year models.
B: ₹2,400 is SI itself.
C: ₹2,520 is CI itself.
D: ₹372 would be the three-year CI−SI difference at these values.

18. Answer B

The first increase is ₹800. The second is 9680−8800=₹880, exactly 10% of ₹8,800. This is annual CI. Check: 8000×1.1^2=₹9,680. Fixed-rate SI would add ₹800 again and give ₹9,600, so it does not match.

Check every option:

A: That base would produce ₹800, not ₹880, in year 2.
B: The year-two interest is 10% of the new base ₹8,800.
C: A fixed rate does not make the two calculation bases identical.
D: The stated fixed rate already explains both annual CI steps.

Use your errors to choose what to revisit

Questions 1, 3, 6, 8, 11 and 14 revisit simple interest: time conversion and amount, unknown rate or principal, amount differences, changing simple rates and multiples. Use the existing Simple Interest lesson and its separate 12-question practice if those steps were difficult
Questions 2 and 9 check the changing CI base and the distinction between amount, period interest and total interest
Questions 4,12 and 15 check period-rate matching. In question 15 the rate is already per half-year
Questions 5 and 10 transfer multipliers to growth or depreciation
Questions 7,13 and 16 reverse the model to find principal, rate or whole-period count
Questions 17 and 18 compare SI and CI under stated matching conditions

Do not only memorise the option letter. Cover the solutions and redo each missed calculation, naming the base and units. Check your result in the forward model. A particular wrong answer may suggest a common mistake, but it does not prove why you chose it.

Sources for further reading

The textbooks support the mathematical models. The RRB list names Simple and Compound Interest and is illustrative, not exhaustive; it does not prescribe these lessons or question counts. The explanations and exercises here are original. The explicit nominal-rate and incomplete-period statements are part of each model, not current financial advice. No recruitment dates, eligibility or logistics are taught here.

Analogy

Before choosing a formula, picture two arithmetic machines. One adds the same amount derived from the original base every period; the other multiplies the latest amount by the same factor every period. The first models fixed-rate SI, the second fixed-period-rate CI. Changing rates require the stated rate at each step; the question’s conditions decide which machine fits.

Quick reference

Mixed review quick reference

Use positive principal P>0. SI time may be fractional after unit conversion. In the CI calculations here, N counts a nonnegative whole number of compounding periods; an incomplete final period needs a separate explicit rule. First identify SI or CI and the requested quantity. Amount equals original principal plus total interest
SI with annual percentage R and time T in years: SI=PRT/100; A=P+SI. Rearrangements require nonzero denominators: P=100 SI/(RT), R=100 SI/(PT), T=100 SI/(PR)
Match time units: annual rates use years, so months divide by 12. A monthly rate instead uses months unless the simple rate itself is converted
With unchanged principal and simple rate: annual interest=(later amount−earlier amount)/(extra years). Subtract the earlier period’s interest to recover P
To become k times the principal, with k≥1, under fixed positive annual SI: required interest=(k−1)P and T=100(k−1)/R. For changing simple rates on the same P, add PR₁T₁/100+PR₂T₂/100+…
CI at fractional rate i per period over N full periods: A=P(1+i)^N; CI=A−P. The next period’s interest uses the latest amount
Only under an explicit nominal annual convention: m=2 for half-years, m=4 for quarters; percentage per period=R/m and N=mT. A rate already quoted per period is not divided again
Exactly two annual periods with matched P and annual rate R: CI−SI=P(R/100)^2. Different durations or conditions require their own calculation
Growth uses current-value multiplier 1+g/100; depreciation uses 1−d/100. Ordinary depreciation has 0≤d≤100; reversing it requires d<100
Reverse principal by dividing by the complete multiplier. For two equal-rate compounding periods, take the positive square root of A/P, subtract 1 and convert to the percentage rate per period. For simple whole-period time questions, recognise a small exact power and check forward
An incomplete final compounding period requires an explicit rule. At zero rate, A=P cannot determine a unique time. Do not guess a model or use SI shortcuts inside CI
These are exact mathematical models with no additional cashflows, fees or taxes. Keep intermediate values exact and check units and direction

Notes for this lesson

Simple and Compound Interest Module Review: Bilingual 18-Question Practice23 pages

Tests for this lesson

Simple and Compound Interest Module Review18 questions · 18 marks · +1 a question
FreeStart: Simple and Compound Interest Module Review

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