Interest

Figure 1: Simple and compound interest are fundamental concepts in finance.

1. Simple Interest

Simple Interest (S.I.) = (P × R × T) / 100

Amount = Principal + Interest

KEY FORMULAS

If rate differs from year to year: S.I. = P × (R₁ + R₂ + R₃ + ...)/100
P = (100 × S.I.) / (R × T)
R = (100 × S.I.) / (P × T)
T = (100 × S.I.) / (P × R)

2. Compound Interest

Amount (A) = P × (1 + r/100)ⁿ

Compound Interest = A - P

KEY FORMULAS

If rate differs from year to year: A = P × (1 + r₁/100) × (1 + r₂/100) × ...
When interest compounded half-yearly: A = P × (1 + r/200)²ⁿ
When interest compounded quarterly: A = P × (1 + r/400)⁴ⁿ
When time is in fraction: A = P × (1 + r/100)ᵗ × (1 + (r/100) × (fractional part))

DIFFERENCE BETWEEN CI AND SI

For 2 years: CI - SI = P × (R/100)²
For 3 years: CI - SI = P × R² × (300 + R) / (100)³

REMEMBER

When a sum doubles itself in n years, rate = (100/n)%
For equal annual instalments: M = n × a + (r × a)/(100 × Y) × n(n-1)/2

3. Exercise (Questions 1-10)

Q1. On what sum of money lent out at 9% per annum simple interest for 6 years does the simple interest amount to ₹810?

(a) ₹900
(b) ₹1000
(c) ₹1200
(d) ₹1500

Answer: (d) P = 810×100/(9×6) = ₹1500

Q2. Out of a certain sum, 1/3 is invested at 3%, 1/6 at 6% and the rest at 8%. If simple interest for 2 years from all investments amounts to ₹600, find the original sum.

(a) ₹4000
(b) ₹5000
(c) ₹6000
(d) ₹7000

Answer: (b) Average rate = (1/3×3 + 1/6×6 + 1/2×8) = 6%. P = 600×100/(6×2) = ₹5000

Q3. On retirement, a person gets 1.53 lakhs of his provident fund which he invests in a scheme at 20% p.a. His monthly income from this scheme will be

(a) ₹2,450
(b) ₹2,500
(c) ₹2,550
(d) ₹2,600

Answer: (c) S.I. = 153000×20/100 = ₹30,600. Monthly = 30600/12 = ₹2550

Q4. A father left a will of ₹68,000 to be divided between his two sons aged 10 years and 12 years such that they get equal amount when each attains age 18. If money is reckoned at 10% p.a., find how much each gets at the time of will.

(a) ₹30,000, ₹38,000
(b) ₹28,000, ₹40,000
(c) ₹32,000, ₹36,000
(d) Cannot be determined

Answer: (c) x(1+10×8/100) = (68000-x)(1+10×6/100). x = 32000, second = 36000

Q5. The price of a T.V. set worth ₹20,000 is to paid in 20 instalments of ₹1000 each. If rate of interest is 6% p.a., and first instalment paid at purchase, then the value of the last instalment covering interest as well will be:

(a) ₹1050
(b) ₹2050
(c) ₹3000
(d) None of these

Answer: (d) Balance = ₹19000. Installment amount can be calculated using annuity formula.

Q6. What sum of money lent out at compound interest will amount to ₹968 in 2 years at 10% p.a., interest being charged annually?

(a) ₹600
(b) ₹700
(c) ₹800
(d) ₹900

Answer: (c) 968 = P(1+0.1)² ⇒ P = 968×100/121 = ₹800

Q7. If the difference between S.I and C.I for 2 years on a sum of money lent at 5% is ₹6, then the sum is:

(a) ₹2200
(b) ₹2400
(c) ₹2600
(d) ₹2000

Answer: (b) Difference = P×R²/10000 ⇒ 6 = P×25/10000 ⇒ P = ₹2400

Q8. A sum of money placed at compound interest doubles itself in 5 years. In how many years will it become 8 times?

(a) 15 years
(b) 20 years
(c) 25 years
(d) 30 years

Answer: (a) (1+r/100)⁵ = 2. For 8 times: (1+r/100)ⁿ = 2³ = (2)³ = [(1+r/100)⁵]³ = (1+r/100)¹⁵ ⇒ n=15 years

Q9. What annual instalment will discharge a debt of ₹4,200 due in 5 years at 10% simple interest?

(a) ₹500 per year
(b) ₹600 per year
(c) ₹700 per year
(d) ₹800 per year

Answer: (c) 4200 = 5a + (10×a×5×4)/(100×2) = 5a + a = 6a ⇒ a = ₹700

Q10. A lent ₹5000 to B for 2 years and ₹3000 to C for 4 years on simple interest at same rate and received ₹2200 in all as interest. The rate of interest per annum is:

(a) 5%
(b) 7%
(c) 7/8%
(d) 10%

Answer: (d) 5000×R×2/100 + 3000×R×4/100 = 2200 ⇒ 100R+120R=2200 ⇒ R=10%

4. Exercise (Questions 11-20)

Q11. The difference between the simple interest received from two different sources on ₹1500 for 3 years is ₹13.50. The difference between their rates of interest is:

(a) 0.1%
(b) 0.2%
(c) 0.3%
(d) 0.4%

Answer: (c) 1500×3×(R₁-R₂)/100 = 13.50 ⇒ R₁-R₂ = 13.50×100/4500 = 0.3%

Q12. An amount of ₹1,00,000 is invested in two types of shares. First yields 9% p.a. and second 11% p.a. If total interest at end of one year is 39/4%, the amount invested in each share was:

(a) ₹52,500, ₹47,500
(b) ₹62,500, ₹37,500
(c) ₹72,500, ₹27,500
(d) ₹82,500, ₹17,500

Answer: (b) 9x/100 + 11(100000-x)/100 = 9750 ⇒ x=62500, second=37500

Q13. A person invested in all ₹2600 at 4%, 6% and 8% per annum simple interest. At end of year, he got same interest in all three cases. The money invested at 4% is:

(a) ₹200
(b) ₹600
(c) ₹800
(d) ₹1200

Answer: (d) 4x = 6y = 8z. x:y:z = 6:4:3. x = 6/13×2600 = ₹1200

Q14. If Re. 1 produces ₹9 in 60 years at simple interest, the rate % p.a. is:

(a) 13⅓%
(b) 14%
(c) 15%
(d) 12½%

Answer: (c) S.I. = 8, P=1, T=60. R = 8×100/(1×60) = 13⅓%

Q15. What sum of money lent out at compound interest will amount to ₹968 in 2 years at 10% p.a., interest being charged annually?

(a) ₹600
(b) ₹700
(c) ₹800
(d) ₹900

Answer: (c) 968 = P(1+0.1)² ⇒ P = ₹800

Q16. If the difference between S.I and C.I for 2 years on a sum of money lent at 5% is ₹6, then the sum is:

(a) ₹2200
(b) ₹2400
(c) ₹2600
(d) ₹2000

Answer: (b) Difference = P×25/10000 = 6 ⇒ P=2400

Q17. What will ₹1000 be worth after three years if it earns interest at 5% compounded annually?

(a) ₹1075
(b) ₹1257
(c) ₹1157
(d) ₹1300

Answer: (c) A = 1000(1.05)³ = ₹1157.625

Q18. A sum of money placed at compound interest doubles itself in 5 years. In how many years will it become 8 times?

(a) 15 years
(b) 20 years
(c) 25 years
(d) 30 years

Answer: (a) n = 5×3 = 15 years

Q19. The C.I. on a certain sum for the 4th year at 8% p.a. is ₹486. What was the C.I. for the third year on the same sum at the same rate?

(a) ₹450
(b) ₹475
(c) ₹456
(d) None of these

Answer: (a) 108% of 3rd year interest = 486 ⇒ 3rd year interest = 486×100/108 = ₹450

Q20. The difference between compound interest and simple interest on a certain sum in 3 years at 7% per annum is ₹225.645. What is the principal?

(a) ₹10,000
(b) ₹15,000
(c) ₹17,000
(d) ₹20,000

Answer: (b) 225.645 = P × 49 × 307 / 1000000 ⇒ P = ₹15,000

5. Exercise (Questions 21-26)

Q21. The simple interest accrued on an amount of ₹19,800 at end of three years is ₹7,128. What would be the compound interest accrued on same amount at same rate in same period?

(a) ₹8934.6784
(b) ₹8017.5744
(c) ₹7861.8754
(d) Cannot be determined

Answer: (b) R = 7128×100/(19800×3) = 12%. C.I. = 19800[(1.12)³ - 1] = ₹8017.5744

Q22. What is the interest received on a sum of ₹450 for 2 years at 10%?

(a) ₹90
(b) ₹180
(c) ₹36
(d) Cannot be determined

Answer: (a) Interest = 450×2×10/100 = ₹90

Q23. Mr. Deepak invested an amount of ₹21,250 for 6 years. At what rate of simple interest will he obtain the total amount of ₹26,350 at end of 6 years?

(a) 4% p.a.
(b) 5% p.a.
(c) 8% p.a.
(d) 12% p.a.

Answer: (a) S.I. = 26350-21250 = 5100. R = 5100×100/(21250×6) = 4%

Q24. Sudhanshu invested ₹15,000 at 10% p.a for one year. If interest compounded every six months, what amount will he get at end of year?

(a) ₹16,537.50
(b) ₹16,500
(c) ₹16,525.50
(d) ₹18,150

Answer: (a) A = 15000(1+5/100)² = ₹16,537.50

Q25. The simple interest accrued on ₹84,000 at end of three years is ₹30,240. What would be the compound interest accrued on same amount at same rate in same period?

(a) ₹30,013.95
(b) ₹31,013.95
(c) ₹34,013.95
(d) ₹33,013.95

Answer: (c) R = 30240×100/(84000×3) = 12%. C.I. = 84000(1.12³ - 1) = ₹34,013.95

Q26. The simple interest accrued on a sum of certain principal is ₹1,200 in four years at 8% p.a. What would be the simple interest accrued on thrice of that principal at 6% p.a in 3 years?

(a) ₹2,025
(b) ₹3,025
(c) ₹2,250
(d) ₹2,150

Answer: (a) P = 1200×100/(4×8) = 3750. S.I. = 3×3750×6×3/100 = ₹2,025

Complete Answer Key

1. (d)	2. (b)	3. (c)	4. (c)	5. (d)
6. (c)	7. (b)	8. (a)	9. (c)	10. (d)
11. (c)	12. (b)	13. (d)	14. (c)	15. (c)
16. (b)	17. (c)	18. (a)	19. (a)	20. (b)
21. (b)	22. (a)	23. (a)	24. (a)	25. (c)
26. (a)

Arithmetic - Interest

Interest

1. Simple Interest

2. Compound Interest

3. Exercise (Questions 1-10)

4. Exercise (Questions 11-20)

5. Exercise (Questions 21-26)

Complete Answer Key

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Arithmetic - Interest

1. Simple Interest

2. Compound Interest

3. Exercise (Questions 1-10)

4. Exercise (Questions 11-20)

5. Exercise (Questions 21-26)

Complete Answer Key

JKAS.IN