UPSC Prelims PYQ › Quantitative Aptitude › Simple & Compound Interest
Simple & Compound Interest — UPSC CSAT Paper II Quantitative Aptitude previous year questions
20 free solved previous year questions on Simple & Compound Interest, papers from 2017 to 2023, drawn from UPSC CDS, UPSC CAPF, UPSC CSAT, covering questions of the kind UPSC asks in CSAT Paper II. Every answer key has been checked again against published sources and solved independently, and each explanation is written fresh.
Read all 20 questions with answers
- #1UPSC CSAT 2023A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal becomes Q in 1 year when compounded annually with S% annual rate of interest, then which one of the following is correct?
- AR = S
- BR > S
- CR < S
- DR ≤ S
Answer: (C) R < SExplanation
Half-yearly compounding at R% gives a growth factor (1 + R/200)^2 = 1 + R/100 + R^2/40000.
Annual compounding at S% gives 1 + S/100.
Equating, S = R + R^2/400, which is larger than R for any positive R.
So R < S.
Answer: option (c).Source: UPSC CSAT 2023 question; answer key checked by independent computation
- #2UPSC CSAT 2018A person bought a refrigerator worth Rs. 22,800 with 12.5% interest compounded yearly. At the end of first year he paid Rs. 8,650 and at the end of second year Rs. 9,125. How much will he have to pay at the end of third year to clear the debt?
- ARs.9,990
- BRs.10,000
- CRs.10,590
- DRs.11,250
Answer: (D) Rs.11,250Explanation
After year 1: 22,800 x 1.125 - 8,650 = 17,000.
After year 2: 17,000 x 1.125 - 9,125 = 10,000.
Payment at end of year 3 = 10,000 x 1.125 = 11,250.
Answer: option (d).Source: UPSC CSAT 2018 question; answer key checked by independent computation
- #3UPSC CDS 2023A person borrowed Rs.10,000 at 12% rate of interest per annum compounded quarterly for a period of 9 months. What is the interest paid by him to settle his account after 9 months?
- ARs.927.27
- BRs.947.47
- CRs.967.67
- DRs.987.87
Answer: (A) Rs.927.27Explanation
Rate per quarter = 3%, and 9 months = 3 quarters.
Amount = 10000 x (1.03)^3 = 10927.27.
Interest = 10927.27 - 10000 = Rs.927.27.
Answer: option (a).Source: UPSC CDS 2023 question; answer key checked by independent computation
- #4UPSC CDS 2023In a business dealing, A owes B Rs.20,000 payable after 5 years, whereas B owes A Rs.12,000 payable after 4 years. They want to settle it now at the rate of 5% simple interest. Who gives how much money in this settlement?
- ABoth are at par
- BB gives Rs. 6,000 to A
- CA gives Rs. 6,000 to B
- DA gives Rs. 4,000 to B
Answer: (C) A gives Rs. 6,000 to BExplanation
Present value of 20,000 due in 5 years = 20000/1.25 = 16,000.
Present value of 12,000 due in 4 years = 12000/1.20 = 10,000.
A's present liability exceeds B's by 6,000, so A pays B 6,000.
Answer: option (c).Source: UPSC CDS 2023 question; answer key checked by independent computation
- #5UPSC CDS 2023What is the difference between simple interest and compound interest on Rs.10,000 for two years at 20% per annum compounded half-yearly ?
- ARs.842
- BRs.756
- CRs.641
- DRs.542
Answer: (C) Rs.641Explanation
Simple interest = 10000 x 20% x 2 = 4,000.
Half-yearly compounding: 10% per period for 4 periods, amount = 10000 x 1.1^4 = 14,641, so CI = 4,641.
Difference = 4641 - 4000 = 641.
Answer: option (c).Source: UPSC CDS 2023 question; answer key checked by independent computation
- #6UPSC CDS 2022If C is the compound interest on Rs. 10,000 for one year at 4% per annum when compounded quarterly, then which one of the following is correct?
- AC < Rs. 100
- BRs. 100 < C < Rs. 200
- CRs. 200 < C < Rs. 400
- DC > Rs. 400
Answer: (D) C > Rs. 400Explanation
Quarterly rate = 1%, number of quarters = 4.
Amount = 10000 x 1.01^4 = 10,406.04, so C = 406.04.
This is more than Rs. 400.
Answer: option (d).Source: UPSC CDS 2022 question; answer key checked by independent computation
- #7UPSC CDS 2022A person borrowed Rs. 9,000 at 7%, Rs. 12,000 at 8% and Rs. 15,000 at 9% simple interest per annum. He had to pay Rs. 50,700 at the end of n years. What is the value of n?
- A3
- B4
- C5
- D6
Answer: (C) 5Explanation
Total principal = 36,000, so total interest = 50,700 - 36,000 = 14,700.
Interest per year = 630 + 960 + 1350 = 2,940.
n = 14,700 / 2,940 = 5.
Answer: option (c).Source: UPSC CDS 2022 question; answer key checked by independent computation
- #8UPSC CDS 2021A sum of money compounded annually doubles itself in 5 years. In how many years will it become four times of itself?
- A10 years
- B12 years
- C15 years
- D20 years
Answer: (A) 10 yearsExplanation
With compound interest the growth factor per 5 years is a constant 2.
Four times is 2 x 2, so two 5-year periods are needed.
Time = 10 years.
Answer: option (a).Source: UPSC CDS 2021 question; answer key checked by independent computation
- #9UPSC CDS 2021A sum of money was invested at simple interest at a certain rate for 5 years. Had it been invested at a 5% higher rate, it would have fetched 500 more. What was the principal amount?
- ARs 2,000
- BRs 1,800
- CRs 1,600
- DRs 1,200
Answer: (A) Rs 2,000Explanation
Extra interest comes only from the extra 5% rate over 5 years.
P x 5% x 5 = 500, so P x 0.25 = 500.
P = 2000.
Answer: option (a).Source: UPSC CDS 2021 question; answer key checked by independent computation
- #10UPSC CDS 2021The difference between the compound interest (compounded annually) and the simple interest on a certain sum of money at 12% per annum for 2 years is Rs.72. What is the principal amount?
- ARs 6,500
- BRs 6,000
- CRs 5,500
- DRs 5,000
Answer: (D) Rs 5,000Explanation
For 2 years, CI - SI = P x (r/100)^2.
So P x 0.0144 = 72.
P = 72/0.0144 = 5000.
Answer: option (d).Source: UPSC CDS 2021 question; answer key checked by independent computation
- #11UPSC CDS 2020The simple interest on a certain sum is one-fourth of the sum. If the number of years and the rate of annual interest are numerically equal, then the number of years is
- A2.5
- B3
- C3.5
- D5
Answer: (D) 5Explanation
SI = P/4 with R = T gives P x T^2/100 = P/4.
T^2 = 25, so T = 5 years.
Answer: option (d).Source: UPSC CDS 2020 question; answer key checked by independent computation
- #12UPSC CDS 2020A sum was put at simple interest at certain rate for 2 years. Had it been put at 1% higher rate of interest, it would have fetched Rs 24 more. What is the sum?
- ARs 500
- BRs 600
- CRs 800
- DRs 1200
Answer: (D) Rs 1200Explanation
The extra 1% rate for 2 years gives extra interest of P x 1 x 2 / 100 = 24.
So P = 24 x 100 / 2 = 1200.
Answer: option (d).Source: UPSC CDS 2020 question; answer key checked by independent computation
- #13UPSC CDS 2019The rate of interest on two different schemes is the same and it is 20%. But in one of the schemes, the interest is compounded half yearly and in the other the interest is compounded annually. Equal amounts are invested in the schemes. If the difference of the returns after 2 years is Rs 482, then what is the principal amount in each scheme?
- ARs 10,000
- BRs 16,000
- CRs 20,000
- DRs 24,000
Answer: (C) Rs 20,000Explanation
Half-yearly: P x 1.1^4 = 1.4641P. Annual: P x 1.2^2 = 1.44P.
Difference = 0.0241P = 482, so P = 20000.
Answer: option (c).Source: UPSC CDS 2019 question; answer key checked by independent computation
- #14UPSC CDS 2019A lent Rs 25,000 to B and at the same time lent some amount to C at same 7% simple interest. After 4 years A received Rs 11200 as interest from B and C. How much did A lend to C?
- ARs 20,000
- BRs 25,000
- CRs 15,000
- DRs 10,000
Answer: (C) Rs 15,000Explanation
Interest from B = 25000 x 7 x 4 / 100 = 7000.
Interest from C = 11200 - 7000 = 4200.
Principal for C = 4200 x 100 / (7 x 4) = 15000.
Answer: option (c).Source: UPSC CDS 2019 question; answer key checked by independent computation
- #15UPSC CDS 2019What is the least number of complete years in which a sum of money put out at 40% annual compound interest will be more than trebled?
- A3
- B4
- C5
- D6
Answer: (B) 4Explanation
We need 1.4^t > 3.
1.4^3 = 2.744 (not enough); 1.4^4 = 3.8416 (more than 3).
Least t = 4 years.
Answer: option (b).Source: UPSC CDS 2019 question; answer key checked by independent computation
- #16UPSC CDS 2019A person divided a sum of Rs. 17,200 into three parts and invested at 5%, 6% and 9% per annum simple interest. At the end of two years, he got the same interest on each part of money. What is the money invested at 9%?
- ARs. 3,200
- BRs. 4,000
- CRs. 4,800
- DRs. 5,000
Answer: (B) Rs. 4,000Explanation
Equal interest for equal time means principals are inversely proportional to rates.
P1 : P2 : P3 = 1/5 : 1/6 : 1/9 = 18 : 15 : 10.
Share at 9% = 17,200 x 10/43 = 4,000.
Answer: option (b).Source: UPSC CDS 2019 question; answer key checked by independent computation
- #17UPSC CAPF 2022Suppose a bank gives an interest of 10% per annum compounded annually for a fixed deposit for a period of two years. What should be the simple interest rate per annum if the maturity amount after two years is to remain the same?
- A10%
- B10.5%
- C11%
- D12%
Answer: (B) 10.5%Explanation
Compound amount on P after 2 years = 1.21P, so the interest is 0.21P.
Simple interest for 2 years at rate r is 2r% of P = 0.21P.
So r = 10.5%.
Answer: option (b).Source: UPSC CAPF 2022 question; answer key checked by independent computation
- #18UPSC CAPF 2021The difference of compound interest and simple interest of a sum of money at the rate of 5% per year for 2 years is Rs.250. The sum is
- ARs.1,00,000
- BRs.80,000
- CRs.40,000
- DRs.1,20,000
Answer: (A) Rs.1,00,000Explanation
For 2 years, CI - SI = P(r/100)^2 = P x 0.0025.
0.0025P = 250, so P = 1,00,000.
Answer: option (a).Source: UPSC CAPF 2021 question; answer key checked by independent computation
- #19UPSC CAPF 2020A sum triples in ten years under compound interest at a certain rate of interest, the interest is being compounded annually. In how many years, it would become nine times?
- A20 years
- B30 years
- C40 years
- D50 years
Answer: (A) 20 yearsExplanation
Tripling takes 10 years, so the growth factor per 10 years is 3.
Nine times = 3 x 3, which needs two such periods.
Time = 20 years.
Answer: option (a).Source: UPSC CAPF 2020 question; answer key checked by independent computation
- #20UPSC CAPF 2017The difference between the compound interest and the simple interest for 2 years on a sum of money is Rs. 60. If the simple interest for 2 years is Rs. 1440, what is the rate of interest?
- A4 1/6 %
- B6 1/4 %
- C8 %
- D8 1/3 %
Answer: (D) 8 1/3 %Explanation
SI for one year = 720.
For 2 years, CI - SI = (one-year SI) x R/100, so 60 = 720 x R/100.
R = 6000/720 = 25/3 = 8 1/3 %.
Answer: option (d).Source: UPSC CAPF 2017 question; answer key checked by independent computation
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