Simple and Compound Interest
17 solved SSC CGL Quantitative Aptitude previous year questions on Simple and Compound Interest, each with the correct answer and a full explanation.
Q1
The difference between compound interest and simple interest on a sum for 2 years at 20 % per annum is Rs. 200. If the interest is compounded half yearly, then what is the difference (in Rs.) between compound and simple interest for 1st year?
✓ Correct answer: a) 50
ExplanationGiven, the difference between C.I and S.I for 2 years at 20% = Rs. 200 Now, CI - SI = When interest is half yearly then R = 10% and Time = 2 years Required difference = 1050 - 1000 = Rs. 50 Hence, Option A is the correct answer.
Q2
If in 2 years at simple interest the principal increases by 18%, what will be the compound interest (in Rs) earned on Rs 7000 in 3 years at the same rate?
✓ Correct answer: b) 2065.2
ExplanationIn 2 years at simple interest the principal increases by 18%.Rate of interest = R = % Now, P = Rs. 7000, T = 3 years and R = 9% CI = P P CI = 7000 CI = 7000 CI = 9065.203 7000 CI = 2065.2 Hence, Option B is the correct answer.
Q3
For an amount, simple interest at the rate of interest of 12% per annum for 6 years is Rs. 25920. What will be the compound interest (in Rs) on same amount at the rate of interest of 8% per annum compounding annually for 2 years?
✓ Correct answer: d) 5990.4
ExplanationGiven, Simple Interest (S.I) after 6 years at 12 % = Rs. 25920 Let, the sum of money (P) = Rs a We know, Simple Interest If Interest is compounded at 8 % for 2 years Amount = Amount = Rs 41990.4 Compound Interest = Amount – Sum of Money (P) = 41990.4 – 36000 = Rs. 5990.4 Hence, Option D is the correct answer.
Q4
If in 3 years at simple interest the principal increases by 18%, what will be the compound interest (in Rs) earned on Rs. 25,000 in 3 years at the same rate?
✓ Correct answer: a) 4775.4
ExplanationGiven,Time = 3 years Let, Principal = 100a According to question Amount after 3 years = 100a 1.18 = 118a Simple Interest = 118a – 100a = 18a We know, Rate = 6 % Now, interest is compounded in 3 years with the same rate.And new principal = Rs. 25,000 Then Amount Compound Interest = Amount – Principal = 29775.4 – 25000 = Rs. 4775.4 Hence, Option A is the correct answer.
Q5
The difference between compound interest and simple interest on ₹ x at 8 % per annum for 2 years is ₹48. What is the value of x ?
✓ Correct answer: b) 7500
ExplanationPrincipal(P)=₹ x Rate of interest(r)=8% Difference between the compound interest and simple interest for 2 years is ₹48. Hence, Option B is the correct answer.
Q6
A person borrowed a sum of ₹30800 at 10% p.a. for 3 years, interest compounded annually. At the end of two years, he paid a sum of ₹13268. At the end of 3rd year, he paid ₹x to clear off the debt. What is the value of x ?
✓ Correct answer: d) 26400
ExplanationA person borrowed a sum of ₹30800 at 10% p.a. 3 years, interest compounded annually.Amount after two years = At the end of two years, he paid a sum of ₹13268. Principal for third year = Rs. 37268 – Rs. 13268 = Rs. 24000 Rate = 10% Amount after 3rd year = At the end of 3rd year, he paid ₹ to clear off the debt.Hence, x = 26400 Hence, Option D is the correct answer.
Q7
A sum of ₹9500 amounts to ₹11495 in 2 years at a certain rate percent per annum, interest compounded yearly. What is the simple interest (in ₹) on the same sum for the same time and double the rate?
✓ Correct answer: c) 3800
ExplanationWe know that: Amount = Principal 11495 = 9500 = r = 10% Now, Simple interest = Therefore, the simple interest on same sum for same time and double the rate = = Rs. 3800 Hence, Option C is the correct answer.
Q8
A loan is to be returned in two equal yearly instalments. If the rate of interest is 10 % p.a., compounded annually and each instalment is ₹ 6534, then the total interest charged (in ₹) is:
✓ Correct answer: c) 1728
ExplanationLet, Where, P = Principal borrowed x = Annual installments R = Rate of interest = Rs. 11340 Hence, Principal borrowed = Rs. 11340 Compound interest = Total installment amount – Principal Hence, Option C is the correct answer.
Q9
A certain sum becomes ₹ 13650 at 15% p.a. simple interest after 2 years. What will be the amount (in ₹ ) of the same sum after 1 year at the same rate of interest, if the interest is compounded half yearly? (nearest to a ₹ )
✓ Correct answer: d) 12134
ExplanationA certain sum becomes ₹13650 at 15% p.a. simple interest after 2 years.Let, principal = Rs. x Simple interest = (Rs. 13650 – Rs. x) Hence, Principal = Rs. 10500 Now, we will calculate the amount (in₹) of the same sum after 1 year at the same rate of interest, if the interest is compounded half- yearly Principal = Rs. 10500 If compounded half-yearly then Time = 2 year Rate = Amount Hence, Option D is the correct answer.
Q10
What is the difference between the compound interest (in ₹) compounded yearly and compounded half yearly for 18 months at 20% per annum on a sum of ₹ 12000 ?
✓ Correct answer: d) 132
ExplanationThe effective rate for compounded yearly at 20% = 20 + 10 + = 32% The effective rate for compounded half yearly at 20% = 10 + 10 + 10 + + = 30 + 3 + 0.1 = 33.1% Therefore, the required difference = = = Rs. 132 Hence, Option D is the correct answer.
Q11
A sum of ₹ 7500 amounts to ₹ 9075 at 10% p.a, interest being compounded yearly in a certain time. The simple interest (in ₹) on the same sum for the same time and the same rate is:
✓ Correct answer: b) 1500
ExplanationA sum of ₹7500 amounts to ₹9075 at 10% p.a, interest being compounded yearly in a certain time.Amount = t = 2 years Hence, Time = 2 years Hence, Option B is the correct answer.
Q12
What is the difference (in ₹) between the simple interest and the compound interest on a sum of ₹ 8000 for years at the rate of 10% p.a., when the interest is compounded yearly?
✓ Correct answer: d) 147.20
ExplanationEffective rate of Simple interest for years = 10 + 10 + 10 = 10 + 10 + 4 = 24% Effective rate of compound interest for years - = = = = 24 + 1.8 + 0.04 = 25.84% Therefore, required difference of compound and simple interest for years = 8000 × = 8000 × = Rs. 147.20 Hence, Option D is the correct answer.
Q13
The interest (in ₹) to be paid on a sum of ₹ 30000 at 15% p.a. after 2 years, if interest compounded yearly, is:
✓ Correct answer: c) 13642.50
ExplanationPrincipal = Rs. 30000 Rate = 15% Time = Interest rate for first 2 years = 15% Interest rate for years = 15 × = 10% Amount after = 30000 × 1.15 × 1.15 × 1.1 = Rs. 43642.5 Compound Interest = 43642.5 - 30000 = 13642.5 The interest to be paid is Rs. 13642.5. Hence, Option C is the correct answer.
Q14
Two equal sums were lent on simple interest at 6% and 10% per annum respectively. The first sum was recovered two years later than the second sum and the amount in each case was Rs.1105. What was the sum (in Rs.) lent in each scheme?
✓ Correct answer: b) 850
ExplanationLet the sum lent in each scheme be ₹x and second sum was lent for y years.Therefore, first sum was lent for (y + 2) years.Now, as per question, Amount in first case = Amount in second case ⇒ (x) + (x) × 6% × (y + 2) = (x) + (x) × 10% × (y) ⇒ (x) × 6 × (y + 2) = (x) + 10y ⇒ 6y + 12 = 10y ⇒ 10y – 6y = 12 ⇒ 4y = 12 ⇒ y = = 3 Now, amount in second case = ₹1105 ⇒ (x) + (x) × 10% × 3 = 1105 ⇒ x + 0.3x = 1105 ⇒ 1.3x = 1105 ⇒ x = = 850 Therefore, the sum lent in each scheme was ₹850. Hence, Option B is the correct answer.
Q15
A certain sum is deposited for 4 years at a rate of 10 % per annum on compound interest compounded annually. The difference between the interest at the end of 2 years and that at the end of 4 years is ₹ 5,082. Find the sum (in ₹ ).
✓ Correct answer: a) 20,000
ExplanationLet, the sum be P Rs. We know that: Compound interest = Effective rate for 4 years at the rate of 10% = 46.41% Effective rate for 2 years at the rate of 10% = 21% Given: Compound interest for 4 years – compound interest for 2 years = 5082 P × - P × = 5082 25.41 P = 508200 P = P = 20000 Rs. Therefore, the sum is 20000 Rs. Hence, the correct answer is (A).
Q16
Simple interest on a certain sum is one-fourth of the sum and the interest rate percentage per annum is 4 times the number of years. If the rate of interest increases by 2%, then what will be the simple interest (in ₹) on ₹5,000 for 3 years?
✓ Correct answer: d) 1,800
ExplanationSimple interest on a certain sum is one-fourth of the sum and the interest rate percentage per annum is 4 times the number of years.Let sum = Rs. X Simple interest = Rs. Let time = t years Rate of interest = 4t % per annum Now, Hence, Rate of interest = Now, Principal = Rs. 5000 Time = 3 years Rate = 10% + 2% = 12% p.a. annum Simple interest = Hence, the correct answer is (D).
Q17
A sum of money at a fixed rate of simple interest amounts to ₹1,630 in 3 years and to ₹ 1,708 in 4 years. Find the sum (in ₹).
✓ Correct answer: c) 1396
ExplanationGiven: Amount in 3 years= Rs.1630 Amount in 4 years = Rs.1708 Formula used: Amount= Principal + n (Simple Interest) Let the Principal be P Amount in 3 years = Rs.1630 P + 3 (S.I.) = Rs. 1630 ......(1) Amount in 4 years = Rs 1708 P + 4 (S.I.) = Rs.1708 ........(2) Subtract (1) from (2) S.I. = 78 Put the value of S.I. IN eq.(1) P + 3 (78) = 1630 P = 1630 234 = Rs.1396 Hence, option C is the correct answer.
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