SIMPLE AND COMPOUND INTEREST

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SIMPLE AND COMPOUND INTEREST

Interest is defined as the cost of borrowing money as in the case of interest charged on a loan balance. Conversely, interest can also be the rate paid for money on deposit as in the case of a certificate of deposit. Interest can be calculated in two ways, Simple interest or Compound interest.

οƒ˜ Simple interest is calculated on the principal or original amount of a loan or deposit.

οƒ˜ Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as "interest on interest."

SIMPLE INTEREST:

If A stands for Amount; P stands for Principal; S.I stands for Simple Interest; T stands for Time (in years); R stands for Rate per cent per year (per annum), then

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COMPOUND INTEREST:

If A stands for Amount; P stands for Principal; C.I stands for Compound Interest; n stands for Time (in years); R stands for Rate per cent per year (per annum), then

1) A = P(1 + 𝑅

100) n

2) C.I = A – P

οƒ˜ If interest is compounded annually but time is in fraction, (Suppose time = 21 5 years), then : A = P (1 + 100R ) Β² Γ— (1 + 1 5R 100)

οƒ˜ When rates are different for different years,say R1%, R2%...Rn% for 1st

year, 2nd year…..nth year respectively, then A = P (1 + R1 100) (1 + R2 100) ……. (1 + Rn 100)

οƒ˜ If Diff. between SI & CI for 2 years is Rs. x, then Principal = (C.I ~ S.I) (100R )

Β²

= x (100R )

Β²

(C.I ~ S.I) = P ( R

100)

Β²

οƒ˜ Diff. between SI & CI for 3 years : (C.I ~ S.I) = P ( R

100)

Β²

Γ— (

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Population :

Let the population of the town be P now and suppose it increases at the rate of R% per annum,then:

οƒ˜ Population after n years = P [1 + R

100 ]

n (After n years population

increases, thus (1 + R

100) is used and if population decreases, (1 βˆ’ R 100) is

used)

οƒ˜ Population n years ago = 𝑃

[ 1 + 𝑅 100 ]𝑛

SOLVED EXAMPLES:

1) Find the Simple Interest on a sum of Rs.2000 at 8% per annum for 3 years? (a) Rs.300 (b) Rs.480 (c) Rs.500 (d) Rs.400 Ans: (b) Rs.480 Formula: S.I = (P Γ— R Γ— T) 100

Given that, Principal P = Rs.2000, Rate R = 8% and Time T = 3 years

Simple Interest, S.I = (P Γ— R Γ— T)

100

S.I = (2000 Γ— 8 Γ— 3)

100

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2) Find the Simple Interest on Rs.4000 for 3 years at the rate of 10% per annum. Also, find the amount.

(a) Rs.1200, Rs.5200 (b) Rs.1600, Rs.4000 (c) Rs.1100, Rs.4400 (d) Rs.1500, Rs.6500 Ans: (a) Rs.1200, Rs.5200 Formula: S.I = (P Γ— R Γ— T) 100 A = P + S.I Given that, Principal P = Rs.4000, Rate R = 10% and Time T = 3 years

Simple Interest, S.I = (P Γ— R Γ— T)

100 S.I = (4000 Γ— 10 Γ— 3) 100 S.I = Rs.1200 Amount, A = P + S.I A = 4000 + 1200 A = Rs.5200

3) Simple interest on a sum at 3 𝟏

𝟐 % per annum in 4 years is Rs.70. Find the sum.

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Ans: (b) Rs.500

Formula: P = S.I Γ— 100

R Γ— T

Given that, Simple Interest S.I = Rs.70, Time T = 4 years and Rate R = 3 1 2 % = 7 2 % Principal, P = S.I Γ— 100 R Γ— T P = 70 Γ— 1005 2 Γ— 4 P = 7000 14 P = Rs.500

4) Pramod took Rs.1100 from Ajay at 8% interest per year. How much will he return to Ajay after 6 months?

(a) Rs.1120 (b) Rs.1088 (c) Rs.1050 (d) Rs.1144 Ans: (d) Rs.1144 Formula: S.I = (P Γ— R Γ— T) 100 A = P + S.I Given that, Principal P = Rs.1100, Rate R = 8%

and Time T = 6 months = 6

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Simple Interest, S.I = (P Γ— R Γ— T) 100 S.I = 1100 Γ— 8 Γ— 1 2 100 S.I = Rs.44 Amount, A = P + S.I A = Rs.1100 + Rs.44 A = Rs.1144

5) At what rate per cent, simple interest will a certain sum of money double itself in 20 years?

(a) 30% (b) 20% (c) 5% (d) 15% Ans: (c) 5% Formula: S.I = A – P R = S.I Γ— 100 P Γ— T

Let the Principal P = Rs.x, Amount A = Rs.2x and Time T = 20 years S.I = A – P

β‡’ S.I = 2x – x β‡’ S.I = Rs.x R = S.I Γ— 100

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R = π‘₯ Γ— 100

π‘₯ Γ— 20

R = 5%

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7) In what time, will the simple interest on the sum of Rs.2600 will be Rs.288 at 8% per annum? (a) 1 5 13 years

(b) 5 years (c) 3 years (d) 2 1 2 years

Ans: (a) 1 5 13 years

Formula: T = S.I Γ— 100 P Γ— R

Given that, Principal P = Rs.2600, Rate R = 8% and Simple Interest S.I = Rs.288 T = S.I Γ— 100 P Γ— R T = 288 Γ— 100 2600 Γ— 8 T = 18 13 years T = 1 5 13 years.

8) Kamal lent Rs.600 to Meena for 2 years and Rs.150 to Anil for 4 years and received altogether from both Rs.90 as simple interest. Find the rate of interest.

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Ans: (a) 5%

Given that, Principal, P1 = Rs.600

Time, T1 = 2 years

Principal, P2 = Rs.150

Time, T2 = 4 years

And Total interest,S.I = Rs.90 P1 x R x T1 100 + P2 x R x T2 100 = 90 600 x R x 2 100 + 150 x R x 4 100 = 90 1200 x R 100 + 600 x R 100 = 90 12 R + 6 R = 90 18 R = 90 R = 90 18 β‡’ Rate of interest, R = 5%

9) What will be the Compound Interest for the sum of Rs.8000 after 3 years at the rate of 5% p.a?

(a) Rs.1320 (b) Rs.1500 (c) Rs.1261 (d) Rs.1100 Ans: (c) Rs. 1261 Formula: A = P (1 + R 100) n C.I = A – P

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Rate R = 5% and Time n = 3 years Amount, A = P (1 + R 100) n = 8000 (1 + 5 100 ) 3 = 8000 ( 105 100 ) 3 = 8000 (21 20 ) 3 = 8000 x 21 20 x 21 20 x 21 20 A = 9261

Compound Interest, C.I = A – P

= 9261 – 8000 = Rs.1261

10) A certain sum amounts to Rs.5832 in 2 years at 8% compound interest. Find the sum.

(a) Rs.6000 (b) Rs.5000 (c) Rs.5500 (d) Rs.4500 Ans: (b) Rs. 5000 Formula: A = P (1 + R 100) n

Given that, Amount A = Rs.5832, Rate R = 8%

and Time n = 2 years Amount, A = P (1 + R

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5832 = P

(1 +

8 100

)

2 5832 = P

(

100 + 8 100

)

2 5832 = P

(

108 100

)

2 5832 = P

(

27 25

)

2 5832 = P x 27 25 x 27 25 P = 5832 x 25 27 x 25 27 P = Rs.5000

11) At what rate percent will a sum of Rs.1000 amount to Rs.1331 in 3 years at compound interest?

(a) 14% (b) 7% (c) 6% (d) 10% Ans: (d) Rs. 10% Formula: A = P (1 + R 100) n

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(11 10) 3 = (1 + R 100) 3 β‡’ 1 + R 100 = 11 10

β‡’ R 100 = 11 10

–

1

β‡’ R 100 = 11 βˆ’ 10 10 β‡’ R 100 = 1 10 β‡’ R = 1 10 x 100 β‡’ Rate of interest, R = 10%

12) Abhay lent Rs.5000 to his friend for 3 years at the rate of 10% per annum compound interest. What amount does Abhay get after 3 years? (a) Rs.6000 (b) Rs.6655 (c) Rs.5665 (d) Rs.5160 Ans: (b) Rs. 6655 Formula: A = P (1 + R 100) n

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= 5000 (22 20 ) 3 = 5000 x 22 20 x 22 20 x 22 20 A = 6655

13) A sum of money deposited at 2% per annum compounded annually becomes Rs.10404 at the end of 2 years. Find the sum deposited. (a) Rs.8000 (b) Rs.10000 (c) Rs.12000 (d) Rs.9000 Ans: (b) Rs. 10000 Formula: A = P (1 + R 100) n

Given that, Amount A = Rs.10404, Rate R = 2%

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14) In how many years, will Rs.6,000 amount to Rs.6,615 compounded annually at the rate of 5% per annum?

(a) 4 years

(b) 8 years

(c) 2 years (d) 10 years

Ans: (c) 2 years

Formula: A = P (1 + R

100) n

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15) The difference between the simple interest and the compound interest(compounded annually) at the rate of 12% per annum for two years is Rs.72. What will be the sum?

(a) Rs.6000 (b) Rs.5400 (c) Rs.6250 (d) Rs.5000

Ans: (d) Rs. 5000

Formula: (C.I ~ S.I) = P

(

𝑅

100

)

2

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