Simple Interest

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[Concept: Basic SI] At what rate of simple interest per annum will a sum of Rs 5000 yield an interest of Rs 2000 in 5 years?

  • 8%
  • 10%
  • 12%
  • 6%
Explanation: Book Formula: R = (SI × 100) / (P × T). Here, P = 5000, SI = 2000, T = 5. R = (2000 × 100) / (5000 × 5) = 200000 / 25000 = 8%.

[Concept: Basic SI] A sum of Rs 8000 is lent at 15% p.a. simple interest. What will be the total amount (A) after 4 years?

  • Rs 12800
  • Rs 12000
  • Rs 4800
  • Rs 13200
Explanation: Formula: SI = (P × R × T) / 100. SI = (8000 × 15 × 4) / 100 = 4800. Total Amount A = P + SI = 8000 + 4800 = Rs 12800.

[Concept: Half-yearly/Quarterly] Find the simple interest on Rs 12000 at 20% p.a. for 1.5 years, if the interest is payable half-yearly.

  • Rs 3600
  • Rs 1800
  • Rs 7200
  • Rs 2400
Explanation: Book Rule: When interest is payable half-yearly, Rate is halved and Time is doubled. R = 20/2 = 10% per half-year. T = 1.5 × 2 = 3 half-years. SI = (12000 × 10 × 3) / 100 = Rs 3600.

[Concept: Half-yearly/Quarterly] A sum of Rs 10000 is invested at 24% p.a. simple interest for 9 months. If the interest is payable quarterly, what is the simple interest?

  • Rs 1800
  • Rs 3600
  • Rs 5400
  • Rs 2400
Explanation: Book Rule: When interest is payable quarterly, Rate becomes one-fourth and Time becomes four times. R = 24/4 = 6% per quarter. Time = 9 months = 3 quarters. SI = (10000 × 6 × 3) / 100 = Rs 1800.

[Concept: Distinct Rates] A sum is lent at 6% p.a. for the first 2 years, 9% p.a. for the next 3 years, and 14% p.a. for the period beyond 5 years. If the total SI earned in 9 years is Rs 11400, what is the principal?

  • Rs 12000
  • Rs 10000
  • Rs 15000
  • Rs 8000
Explanation: Book Formula: Total SI = P(R1T1 + R2T2 + R3T3)/100. Let Principal be 100%. Total Effective Rate = (6×2) + (9×3) + (14×4) = 12 + 27 + 56 = 95%. So, 95% of P = 11400. P = (11400 / 95) × 100 = Rs 12000.

[Concept: Distinct Rates] A man invests a sum at 5% p.a. for 3 years, 8% p.a. for 4 years, and 10% p.a. for the next 2 years. If the total interest earned is Rs 6030, find the sum.

  • Rs 9000
  • Rs 8000
  • Rs 10000
  • Rs 7500
Explanation: Total Effective Rate% = (5×3) + (8×4) + (10×2) = 15 + 32 + 20 = 67%. We are given that 67% of Principal = 6030. P = (6030 / 67) × 100 = 90 × 100 = Rs 9000.

[Concept: Sum becomes ‘n’ times] A certain sum of money becomes 4 times of itself in 15 years at simple interest. What is the rate of interest per annum?

  • 20%
  • 25%
  • 15%
  • 30%
Explanation: Book Formula: If a sum becomes ‘n’ times of itself, R% = [(n – 1) / T] × 100%. Here n = 4, T = 15. R = [(4 – 1) / 15] × 100% = (3 / 15) × 100% = 1/5 × 100% = 20%.

[Concept: Sum becomes ‘n’ times] At what time will a sum of money become 5 times of itself at a simple interest rate of 16% per annum?

  • 25 years
  • 20 years
  • 30 years
  • 16 years
Explanation: Book Formula: T = [(n – 1) / R] × 100. Here n = 5, R = 16. T = [(5 – 1) / 16] × 100 = (4 / 16) × 100 = 1/4 × 100 = 25 years.

[Concept: SI becomes ‘n’ times] In how many years will the simple interest on a sum of money be equal to 3 times the principal at a rate of 12% per annum?

  • 25 years
  • 20 years
  • 15 years
  • 30 years
Explanation: Book Formula: If SI becomes ‘n’ times of Principal (SI = P × n), then RT = n × 100. Here, n = 3, R = 12. 12 × T = 3 × 100. 12T = 300. T = 300 / 12 = 25 years.

[Concept: SI becomes ‘n’ times] If the simple interest on a certain sum is 1.5 times the principal in 10 years, what is the rate of interest per annum?

  • 15%
  • 10%
  • 20%
  • 12%
Explanation: Book Formula: RT = n × 100. Here n = 1.5 and T = 10. So, R × 10 = 1.5 × 100. 10R = 150. R = 15%.

[Concept: Difference in SI] The difference between the simple interest received from two different banks on Rs 5000 for 2 years is Rs 25. Find the difference between their rates of interest.

  • 0.25%
  • 0.5%
  • 1%
  • 0.75%
Explanation: Book Formula: P = (Diff in SI × 100) / (Diff in Rate × Time). So, Diff in Rate = (Diff in SI × 100) / (P × Time) = (25 × 100) / (5000 × 2) = 2500 / 10000 = 0.25%.

[Concept: Difference in SI] If the simple interest on a certain sum for 4 years at 8% p.a. is Rs 320 less than the SI on the same sum for 6 years at 7% p.a., find the sum.

  • Rs 3200
  • Rs 4000
  • Rs 2500
  • Rs 3600
Explanation: Effective Rate 1 = 4 × 8% = 32%. Effective Rate 2 = 6 × 7% = 42%. Difference in effective rates = 42% – 32% = 10%. We are given that this 10% of Principal = Rs 320. Thus, 100% of Principal = 320 × 10 = Rs 3200.

[Concept: Amounts to A & B in diff years] A sum lent at simple interest amounts to Rs 6000 in 2 years and Rs 7500 in 5 years. Find the principal sum.

  • Rs 5000
  • Rs 4000
  • Rs 4500
  • Rs 5500
Explanation: Book Formula: P = (A·t2 – B·t1) / (t2 – t1). Here A=6000, t1=2, B=7500, t2=5. P = (6000×5 – 7500×2) / (5 – 2) = (30000 – 15000) / 3 = 15000 / 3 = Rs 5000. (Or simply, SI for 3 yrs = 1500, so SI for 1 yr = 500, SI for 2 yrs = 1000. P = 6000 – 1000 = 5000).

[Concept: Amounts to A & B in diff years] A certain sum amounts to Rs 1008 in 2 years and to Rs 1164 in 3.5 years at simple interest. What is the rate of interest per annum?

  • 13%
  • 12%
  • 14%
  • 15%
Explanation: Book Formula: R% = [(B – A) × 100] / [A·t2 – B·t1]. Here A=1008, t1=2, B=1164, t2=3.5. R% = [(1164 – 1008) × 100] / [(1008×3.5) – (1164×2)] = 15600 / (3528 – 2328) = 15600 / 1200 = 13%.

[Concept: Installments] What annual equal installment will discharge a debt of Rs 6450 due in 4 years at 5% simple interest?

  • Rs 1500
  • Rs 1600
  • Rs 1400
  • Rs 1612.5
Explanation: Book Formula: Installment = (A × 200) / [T(200 + (T-1)r)]. Here A=6450, T=4, r=5. Installment = (6450 × 200) / [4(200 + 3×5)] = 1290000 / [4(215)] = 1290000 / 860 = Rs 1500.

[Concept: Installments] A debt of Rs 4200 is to be paid in 5 equal annual installments at 10% simple interest. Find the value of each installment.

  • Rs 700
  • Rs 840
  • Rs 800
  • Rs 750
Explanation: Book Formula: Installment = (A × 200) / [T(200 + (T-1)r)]. Here A=4200, T=5, r=10. Installment = (4200 × 200) / [5(200 + 4×10)] = 840000 / [5(240)] = 840000 / 1200 = Rs 700.

[Concept: Recurring Deposit (RD)] A person deposits Rs 500 per month for 2 years in a recurring deposit account. If he receives an interest of Rs 1500 at maturity, what is the rate of interest per annum?

  • 12%
  • 10%
  • 8%
  • 15%
Explanation: Book Formula: r = (SI × 2400) / [n(n+1) × deposited_amount], where n is number of months. Here SI=1500, n=24, Amt=500. r = (1500 × 2400) / [24 × 25 × 500] = 3600000 / 300000 = 12%.

[Concept: Recurring Deposit (RD)] An amount of Rs 200 is deposited monthly for 1 year. If the total simple interest earned is Rs 156, what is the rate of interest per annum?

  • 12%
  • 10%
  • 14%
  • 15%
Explanation: Book Formula: r = (SI × 2400) / [n(n+1) × deposited_amount]. Here SI=156, n=12, Amt=200. r = (156 × 2400) / [12 × 13 × 200] = 374400 / 31200 = 12%.

[Concept: Diff between SI for two sums] Find the difference between the simple interest on Rs 4000 at 5% p.a. for 4 years and the simple interest on Rs 3000 at 8% p.a. for 3 years.

  • Rs 80
  • Rs 100
  • Rs 120
  • Rs 50
Explanation: Book Formula: SI diff = (P2·R2·T2 – P1·R1·T1)/100. SI_1 = (4000×5×4)/100 = 800. SI_2 = (3000×8×3)/100 = 720. Difference = 800 – 720 = Rs 80.

[Concept: Diff between SI for two sums] The simple interest on Rs P at 10% for 3 years is Rs 300 more than the simple interest on Rs 5000 at 6% for 2 years. Find the value of P.

  • Rs 3000
  • Rs 4000
  • Rs 2500
  • Rs 3500
Explanation: SI on Rs 5000 = (5000×6×2)/100 = Rs 600. Since the SI on P is Rs 300 more, SI on P = 600 + 300 = Rs 900. Now, (P × 10 × 3)/100 = 900. 30P / 100 = 900. P = (900 × 100) / 30 = Rs 3000.

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