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Given:

If the Rs. 7500 taken at 8% compound interest is to be repaid in equal annual installment of 3 years

Formula used:

P(1 + R/100)^T = x + x(1 + R/100) + x(1 + R/100)²................+ x(1 + r/100)^{(n – 1)} 

P = principal, R = rate per annum, T = time

Calculation:

Let be the each installment be Rs. x

According to the question,

⇒ 7500(1 + 8/100)³ = x + x(1 + 8/100) + x(1 + 8/100)²

⇒ 7500 × 1.08³ = x + 1.08x + 1.664x

⇒ 9447.84 = 3.2462x

⇒ x = 9447.48/3.2464

⇒ x = 2910(Approx)

∴ The approximate annual installment is Rs. 2910.

Given:

Total amount to invest = Rs. 8425

Ages of sons are 24 years and 28 years.

Formula used:

A = P(1 + r/100)ⁿ

Where, A = Amount

P = Principal

r = Rate

n= time

Calculation:

Let Principal of younger daughter be (P1) 

And, Let Principal of elder daughter be (P₂)

Time of elder daughter = (40 – 28) years = 12 years

Time of younger daughter = (40 – 24) years = 16 years

Rate = 33.3% = (100/3)%

According to the question:

Younger daughter = Elder daughter

P₁(1 + r/100)n = P₂(1 + r/100)n

⇒ P1[1 + (100/3 × 100)]¹⁶ = P2[1 + 100/3 ×100)]¹²

⇒ P1(4/3)16 = P2(4/3)12

⇒ P₁/P₂ = [(4/3)12/(4/3)16]

⇒ P1/P2 = [1/(4/3)⁴]

⇒ P1/P2 = (3/4)4

⇒ P1/P2 = 81/256

⇒ P1 : P2 = 81 : 256

Now, again let P₁ be 81x

Let P₂ be 256x

Total principal = (81x + 256x) = Rs. 337x

Again,

⇒ 337x = 8425

⇒ x = 8425/337 

P₁ = 256x = 256 × (8425/337) = Rs. 6400

∴ The share of elder daughter is Rs. 6400.

Given:

Compound interest = Rs. 4,070

Rate = 5.55%

Time = 2 years

Concept used:

11.11% = 1/9 

Formula used:

C.P = P{(1 + R/100)T – 1}

Where, 

C.P → Compound interest 

P → Principal 

R → Rate 

T → Time 

Calculations:

11.11% = 1/9 

⇒ (11.11%)/2 = 1/(9 × 2)

⇒ 5.55% = 1/18

Now, C.I. = P{(1 + R/100)^T – 1}

⇒ 4070 = P{(1 + 5.55/100)² – 1)}

⇒ 4070 = P {(1 + 1/18)² – 1}

⇒ 4070 = P{(19/18 × 19/18) – 1}

⇒ 4070 = P{(361 – 324)/324}

⇒ 4070 = P × (37/324)

⇒ P = (4070 × 324)/37

⇒ 110 × 324

⇒ Rs. 35,640

∴ The principal is Rs. 35,640 

Given:

Principal = Rs. 9500

Amount = Rs 10,070

Rate = 3 % per annum

Formula used:

S.I = ( P × R × T)/100

Calculation:

S.I = Amount – Principal

⇒ 10,070 – 9,500

⇒ Rs. 570

570 = (9500 × 3 × T)/100

⇒ (570 × 100)/(9500 × 3) = T

⇒ T = 2 years

∴ The required time is 2 years

Given:

Amount = Rs. 11550

Principal = Rs. 7500

Rate of interest = 13.5%

Formula Used:

Simple interest = Amount – Principal

Simple interest = Principal × Rate of interest/100 × Time

Calculation:

Simple interest = Amount – Principal

⇒ 11,550 – 7500

⇒ 4,050

Simple interest = Principal × Rate of interest/100 × Time

⇒ 4,050 = 7500 × (13.5/100) × Time

⇒ Time = 4 years

∴ In 4 years Rs. 7500 becomes Rs. 11550 @ 13.5% p.a.

Given:

Principal = Rs 625,

Amount = Rs 1296,

Time period = 1 year or 4 quarters

Formula Used:

A = P{1 + (r/100)}n

where, A = Amount, P = Principal, r = Rate% and n = Time or number of periods

Calculation:

Here,

A = P{1 + (r/100)}4

⇒ 1296 = 625 × {1 + (r/100)}4

⇒ 1296/625 = {1 + (r/100)}⁴

⇒ (6/5)⁴ = {1 + (r/100)}⁴

When LHS = RHS with same power then bases should be equal.

⇒ (6/5) = 1 + (r/100)

⇒ (6/5) - 1 = r/100

⇒ 1/5 = r/100

⇒ r = 20%

As we have taken time period as 4 quarters, so the rate we calculated is per quarter.

So Rate % per annum = 20 × 4 = 80% per annum.

∴ The Rate percent per annum is 80%.

Given:

Difference C.I and S.I for 2 years = Rs. 22.50

Time = 2 years

Principal = Rs. 1000

Formula used:

Difference C.I and S.I for 2 years = (principal × r²)/10000

Calculation:

22.50 = (1000 × r²)/10000

⇒ r2 = 225

⇒ r² = 15²

⇒  r = 15

∴ The rate of interest per annum is 15%.

Given:

A certain sum is invested under simple interest for 9 years at a certain rate of interest.

Had the rate of interest been 1% more, the interest for 9 years would have been Rs. 234 more.

Formula:

S.I = PRT/100

Where, P = Principal

R = Rate of interest

T = Time taken

Calculation:

Let the sum be P and rate of interest be r

[(P × r × 9)/100] + 234 = [P × (r + 1) × 9]/100

⇒ 234 = P × (9/100)

⇒ P = 234 × (100/9)

⇒ P = Rs. 2600

∴ The sum is Rs. 2600

Given:

Interest = 6/5 times of principal

Rate of interest = 20%

Formula used:

SI = (P × R × T)/100

where I = Interest, P = Principal, R = Rate and T = Time

Explanation:

Let principal = x then,

Interest = x × 6/5 = 6x/5

6x/5 = (x × 20 × T)/100

⇒ 6x/5 = (x × T)/5

⇒ T = 6 years

∴ The time will be 6 years.

Given:

SI = 1/5 × P

T = 4 yr

Formula used:

SI = P × R% × T

Calculation:

SI = P × R% × T

⇒ 1/5 × P = P × R/100 × 4

⇒ 20/4 = R

⇒ R = 5%

∴ The rate of interest per annum is 5%.

Given:

Number of days = 120 days

Principal = Rs 4800

Rate of interest = 10%

Concept used:

Simple interest, SI = P × R × T/100

Calculation:

SI = 4800 × (120/365) × (10/100) = Rs. 157.80

∴ The simple interest obtained is Rs 157.80.

Given:

The principal of each person is Rs.43892.

The first on SI at rate of 30% for 3 years.

The second on CI at rate of 30% for 3 years.

Formula Used:

SI = P × R × T/100

Amount = P[1 + R/100]ⁿ

CI = Amount - Principal

Calculation:

The principal of each person is Rs.43892.

The first on Simple Interest at rate of 30% for 3 years.

Simple Interest = 43892 × 30 × 3/100 = Rs.39502.8

The second on Compound Interest at rate of 30% for 3 years.

Amount = 43892[1 + 30/100]³

⇒ 43862 × 130/100 × 130/100 × 130/100

⇒ Rs.96364.81

Compound Interest= 96364.81 - 43892 = Rs.52472.81

The difference between Compound Interest and Simple Interest = Rs.12970.01

The percentage = 12970.01/52472.81 × 100 = 24.7%

∴ The percentage simple interest be less than the compound interest is 24.7%. 

Given:

Difference between C.I. and S.I. for 3 years : Difference between C.I. and S.I. for 2 years = 31 : 10

Formula used:

Difference between C.I. and S.I. for 3 years = P(R/100)²(300 + R)/100

Difference between C.I. and S.I. for 2 years = P(R/100)²

Calculations:

Difference between C.I. and S.I. for 3 years : Difference between C.I. and S.I. for 2 years = 31 : 10

\(\Rightarrow \;\frac{{P{{\left( {\frac{R}{{100}}} \right)}^2}\left( {\frac{{300\; + \;R}}{{100}}} \right)\;}}{{P{{\left( {\frac{R}{{100}}} \right)}^2}}}\; = \;\frac{{31}}{{10}}\)

⇒ (300 + R)/100 = 31/10

⇒ 3000 + 10R = 3100

⇒ 10R = 100

⇒ R = 10%

∴ The required rate is 10%

Given:

Principal = Rs.13000 

Rate of interest = 15%

Effective rate of interest = 15 × 8/12 = 10%

and 2 years = 24 months = 3 eight monthly

Formula:

Let P = Principal, R = rate of interest and N = time period

Compound interest = P(1 + R/100)³  - P

Calculation:

∴ Compound interest = 13000(1 + 10/100)³  - 13000 = Rs.4303

For compound interest calculated eight monthly

R = (original rate) × 8/12

Time convert into months.

Given:

Principal = Rs. 1000

Rate = 10%

Time = 3 years

Formula Used:

Compound Interest = \(P( 1 + {R \ \over 100})^T - P\)

Calculation:

C.I = P (1 + \( {10 \ \over 100}\))^T - P

⇒ 1000 × (\( {11 \ \over 10}\))³ - 1000

⇒ 1331 - 1000

⇒ Rs.331

∴ The required compound interest is Rs 331

Concept: Compound Interest = Amount - Principle

where Amount = P(1 + R/100)ⁿ

Solution:

Given: Principle = 1000

Rate = 10%

Time = 2 years

Using the above formula, we get,

CI = 1000(1 + 10/100)² - 1000

10000(121/100) - 1000

1210 - 1000 = 210

Hence, we conclude that the compound interest is 210.

Given:

P = 7500

R = 4%

T = 2 years

At compound interest

Formula:

A = \(P\left( {1 + \frac{r}{{100}}} \right)\)^t

where,

A = Amount

P = Principle 

r =  Rate

T = Number of years

Calculation:

A = \(P\left( {1 + \frac{r}{{100}}} \right)\)t

⇒ A = 7500(1 + 4/100)² 

⇒ A = 7500 (26/25)²

⇒ A = 7500 × 26/25 × 26/25

⇒ A = 12 × 26 × 26

⇒ A = 8112

Population of the city 3 years ago = P = 128000 and n = 3

And, the decreasing percentage = R = 5%

The present population = P x (1 - R/100)ⁿ

= 128000 x (1 - 5/100)³

= 128000 x 19/20 x 19/20 x 19/20

= 16 x 6859 = 109744.

GIVEN:

Principal = Rs. 640000

Rate = 5% per annum

Time = 3 years

CONCEPT:

It is a question of Compound interest where we have to find the final amount, Time period is 3 years and the rate of interest is given as 5% pa.

FORMULA USED:

A = P × [1 + (R/100)]^T

CALCULATION:

Applying the formula:

Amount = \(640000{\left( {1 + \frac{5}{{100}}} \right)^3} = 80 \times {21^3} = 740880\)

∴ Amount is Rs. 7,40,880.

Given:

Rate of interest for first year = 5%

Rate of interest for second year = 10%

Time = 3 years

Amount = Rs. 1,03,950

Principal = Rs. 75,000

Concept used:

A = P(1 + R₁/100)(1 + R₂/100)(1 + R₃/100)

Where,

A → Amount

P → Principal 

R → Rate 

Calculations:

A = P(1 + R1/100)(1 + R2/100)(1 + R3/100)

⇒ 103950 = 75000(1 + 5/100)(1 + 10/100)(1 + R₃/100)

⇒ 103950 = 75000 × (21/20)(11/10)(1 + R₃/100)

⇒ 103950 = 86625 × (1 + R₃/100)

⇒ 103950/86625 = (1 + R₃/100)

⇒ 1.2 × 100 = 100 + R₃

⇒ 120 = 100 + R₃

⇒ R₃ = 20%

∴ Rate of interest for the third year is 20%

Given:

The simple interest for a second year = Rs. 1000

Concept used:

A simple interest in every year is always the same.

Calculation:

Simple interest on 6th year = Rs. 1000

Simple interest on 7th year = Rs. 1000

Simple interest on 8th year = Rs. 1000

The sum of the interest accrued on it for the 6th, 7th and 8th years = Rs. (1000 + 1000 + 1000)

⇒ The sum of the interest accrued on it for the 6th, 7th and 8th years = Rs. 3000

∴ The sum of the interest accrued on it for the 6th, 7th and 8th years is Rs. 3000.

Given

Principle = 2500

Rate = 5%

Time = 219 days

Formula

SI = P × R × T/100

Calculation

Time = 219 days = 219/365 years = 3/5 years

SI = [2500 × 5 × (3/5)]/100

⇒ 25 × 3

⇒ 75 

∴ The simple interest is 75.

GIVEN:

Principal = Rs. 500, R = 20% and T = 1

CONCEPT:

When interest is compounded half-yearly:

Time = 1 × 2 = 2

Rate = 20/2 = 10%

FORMULA USED:

A = P × [1 + R/100]^T

CALCULATION:

Applying the formula:

A = 500 × [1 + 10/100]²

= 500 × 1.21

= 605

Hence,

Given:

The sum of money is Rs. 2000 which becomes Rs. 2420 at 10% per annum

Formula used:

Amount = p × (1 + r/100)ⁿ

Calculation:

Let the time period be t

Amount = p × (1 + r/100)n

⇒ 2420 = 2000 × (1 + 10/100)^t

⇒ 2420/2000 = (11/10)^t

⇒ (121/100) = (11/10)^t

⇒ (11/10) ² = (11/10)^t

⇒ t = 2 years

∴ The time is 2 years.

Given:

Principal (P) = Rs. 12,000

Rate of interest (R) = 10%

Amount (A) = Rs. 20,400

Formula used:

A = P + SI

SI = (P × R × T)/100

Where P is Principal, R is Rate of interest, T is Time and SI is Simple Interest

Calculation:

A = P + SI

20400 = 12000 + SI

⇒ SI = 20400 – 12000 = 8400

SI = (P × R × T)/100

⇒ 8400 = (12000 × 10 × T)/100

⇒ 8400 = 1200 × T

⇒ T = 8400/1200 years

⇒ 7 years

∴ Time is 7 years

Given

Principle = 400

Amount = 480

Time = 4 years

Formula used:

SI = (P × R × T) / 100

Calculation:

SI = Amount - Principal

⇒ 480 - 400

⇒ Rs.80

SI for 1 year = 80/4

⇒ Rs.20

⇒ Rate = (SI × 100)/ P × T

⇒ Rate = (20 × 100)/ 400 × 1

⇒ Rate = 5%

∴ New rate = 5% + 2% = 7%

⇒ SI = (400 × 7% × 4)/100

⇒ SI = Rs.112

Amount = Principle + Simple interest

⇒ 400 + 112

⇒ Rs.512

Given:

Sum of money = Rs. 6,250

Rate of interest = 16%

C.I. is compounded quarterly for 9 months.

Concept used:

Amount = P × (1 + R/400)^4T

Calculation:

⇒ Rs. 6,250 × (1 + 16/400)(^{9/12) × 4} 

⇒ Rs. 6,250 × (1 + 0.04)3

⇒ Rs. 6,250 × 1.124864 

⇒ Rs. 7030.4 

∴ The amount rises to Rs. 7,030.4 when compound interest is earned at 16% p.a., compounded quarterly for 9 months

Given:

Principal = Rs. 2744

Time = 2 years

Rate = (100/7)%

Concept used:

C.I. = P{(1 + R/100)^T – 1}

S.I. = (P × R × T)/100

S.I. → Simple interest

P → Principal

T → Time

R → Rate%

C.I. → Compound interest

Calculation:

S.I. = (P × R × T)/100 = (2,744 × (100/7) × 2)/100 = 784

C.I. = P{(1 + R/100)T – 1}

⇒ C.I. = 2,744(1 + 100/700)² – 2,744

⇒ C.I. = 2,744 × (8/7) × (8/7) – 2,744

⇒ C.I. = 3,584 – 2,744

⇒ C.I. = 840

C.I. + S.I. = Rs. (840 + 784) = Rs. 1,624

∴ The sum of C.I. and S.I. is  Rs. 1,624

Given:

Rate = 20%

Formula used:

SI = (P × R × T)/100

For CI,

Amount = P(1 + r/100)n

Amount = P + CI

Here n is the time

Concept used:

In case of half yearly, the rate is half and time is doubled

CI and SI is same for first year

Calculation:

Let the sum be x

CI for half yearly

Rate = 20%/2 = 10%

Amount = P(1 + r/100)n

⇒ x(1 + 10/100)2

⇒ 121x/100

CI = 121x/100 – x = 21x/100

And for yearly,

SI = CI = (x × 20 × 1)/100

⇒ 20x/100

Now, A/Q,

21x/100 – 20x/100 = 757.8

⇒ x = 75780

Now, SI = (75780 × 20 × 1.5)/100 = 22734

∴ The required simple interest is Rs 22734 

Given:

Principal (P) = Rs.50,000

C.I. = Rs.11,605

Rate (R) = 11%

Formula used:

A = P(1 + R/100)n

Where A → amount

P → principal

R → rate 

n → time

Calculations:

Amount = 50000 + 11605 = Rs. 61,605

A = P(1 + R/100)n

⇒ 61605 = 50000(1 + 11/100)ⁿ

⇒ (111/100)n = 61605/50000

⇒ (111/100)n = 12321/10000

⇒ (111/100)n = (111/100)²

⇒ n = 2

∴ The time period is 2 years.

Interest received on simple interest at12% for 3 years

SI = (P × R × T)/100

P → Principle amount

R → Rate

T → Time

⇒ SI = (P × 12 × 3)/100 = 36P/100 = 0.36P

Interest received on compound interest at 12% for 3 years

CI = P{1 + (R/100)}^t – P

⇒ CI = P(1 + 12/100)³ – P = P{(1.12)³ – 1} = 0.404928P

According to question,

⇒ 0.404928P – 0.36P = 1123.2

⇒ 0.044928P = 1123.2

⇒ P = 25000

∴ The amount deposited by the man.is Rs.25000

Given

Compound interest - Simple interest = 360

Formula used

If the difference between the compound and simple interest is given and rate of interest is given, then formula for calculating principal is as follows:

C.I - S.I = P(R/100)²

P, R and T are principal and rate.

Calculation

360 = P(6/100)²

(360 × 100 × 100)/(6 × 6) = P

P = Rs.1,00,000

∴ The principal is Rs.1,00,000.

Given:

P = 1500 Rs.

R = 14%

T = 1 year

Formula used : 

\(Amount = \;\frac{{P\; \times \;\left( {100 + R \times T} \right)}}{{100}}\)

Calculation:

\(Amount = \;\frac{{1500\; \times \;\left( {100 + 14 \times 1} \right)}}{{100}}\)

⇒ 15 × 114

⇒  Rs. 1,710

∴ The amount is Rs. 1,710.

Given:

A sum amounts to Rs. 6,050 in 2 years and to Rs. 6,655 in 3 years at a certain rate percentage p.a. when the interest is compounded yearly.

Formula:

Let P = Principal, R = rate of interest and N = time period

Simple interest = PNR/100

Compound interest = P(1 + R/100)ⁿ - P

Calculation:

Accordingly,

6050 = P(1 + R/100)²

And, 6655 = P(1 + R/100)³

Dividing,

(1 + R/100) = 6655/6050

⇒ R/100 = 6655/6050 - 1

⇒ R/100 = 605/6050

⇒ R = 10%

Simple interest on a sum of Rs. 6,000 at the same rate for 5\(\frac{3}{4}\) years = 6000 × 10/100 × 23/4

⇒ Rs.3450

∴ Required simple interest is Rs. 3450

Given:

Amount = Rs. 6,050

Time = 2 years

Rate of interest = 10% p.a.

Formula Used:

[(100 + Rate of interest)/100]^Time = (Amount/Principal)

Compound Interest = Amount - Principal

Calculation:

Let assume that Principal = x

So,

[(100 + Rate of interest)/100]Time = (Amount/Principal)

⇒ [(100 + 10)/100]² = (6050/ x)

⇒ (110/100) × (110/100) = (6050/ x)

⇒ (121/100) = (6050/x)

By cross multiplying

⇒ x = 6050 × (100/121)

⇒ x = 5,000

Compound Interest = Amount - Principal

⇒ Compound Interest = 6,050 - 5,000

⇒ Compound Interest = Rs. 1,050

∴ The compound interest is Rs. 1,050

The correct option is 2 i.e. Rs. 1,050

Given:

A₁ = Rs. 3600, N₁ = 3 years

A₂ = Rs. 4800, N₂ = 6 years

Formula used:

A = P × {1 + (R/ 100)}^N

Where P = Principal amount, R = Rate of interest in %, N = Number of years

Calculation:

Assuming Rate of compound interest = R% and principal amount = Rs. X

Now, according to equation

⇒ 3600 = X × {1 + (R / 100)}³   ----(1)

⇒ 4800 = X × (1 + (R / 100)) ⁶   ----(2)

Dividing Equation 2 by Equation 1

⇒ 4800/3600 = {1 + (R / 100)}³

⇒ 4 / 3 = {1 + (R / 100)}³   ----(3)

Substituting Equation (3) in Equation (1)

⇒ 3600 = X × (4 / 3)

⇒ 3600 × (3 / 4) = X

⇒ 2700 = X

Given:

Difference between compound interest and simple interest = Rs. 940

Time = 2 years

Rate of interest = 20%

Concept used:

D = P × (R/100)²

Where,

D → Difference between C.I. and S.I. for 2 years 

P → Principal 

R → Rate 

Calculations:

D = P × (R/100)2

⇒ 940 = P × (20 × 20)/(100 × 100)

⇒ 940 = P × 1/25

P = 940 × 25 = Rs. 23,500

∴ The principal is Rs. 23,500

Given:

Principal Amount (P) = Rs. 4400

Time Period (T) = 2 years

Compound Interest after two years (CI) = 1119.36

Formulae Used:

If Principal = P,  Time period = T, and Rate of Interest = R;

Compound Interest (CI) = {P [1 + (R/100)]T} - P; and 

Simple Interest (SI) = (P × R × T)/100

Calculation:

Using the formula for CI, we can obtain the rate of interest (R) as:

Compound Interest (CI) = {P [1 + (R/100)]T} - P

⇒ 1119.36 = {4400 × [1 + (R/100)]2} - 4400

⇒ 5519.36/4400 = [(100 + R)/100]²

⇒ (100 + R)² = 1.2544 × 10000

⇒ (100 + R) = 112

⇒ R = 12%

Now, for calculating the Simple Interest,

Rate of Interest remains the same, so Rate = R

Time period doubles, so T = 4 years

Hence, we can calculate the value of Simple Interest (SI), as:

SI = (4400 × 12 × 4)/100

⇒ SI = Rs. 2112

∴ The simple interest on the sum ​at the same rate for double the time is Rs. 2112

Given:

Principal = Rs. 14000, S.I. = Rs. 1260, Rate= 3% per annum, Time = t years

Formula used:

S.I. = (P × R × T)/100

C.I. = P[(1 + (r/100))^t – 1]

Calculation:

1260 = (14000 × 3 × t)/100

⇒ t = 3 years

C.I. = 14000 [(1 + (10/100))³ – 1]

⇒ 14000 [(11/10)³ – 1]

⇒ 14000 × (331/1000)

⇒ Rs.4634

Given

Principal = Rs.18,000; Rate = 7% per an um ; Time = 8 months

Formula used

Simple interest = (p × r × t)/100

Where p, r and t are principal, rate of interest and time.

Concept

When time is given in months it is converted into year by dividing the given months by 12

Calculation

Simple interest = (18,000 × 7 × 8)/(100 × 12)

⇒  Rs.840

∴ The simple interest is Rs.840.

Given:

Amount = Rs. 2188.68

Time period = 8 years

Rate of interest = 7%

Formula used:

SI = (P × R × T)/100

A = P + SI

Where,

SI = Simple interest

P = Sum of money invested

R = Rate of interest

T = Time period of investment

A = Amount

Calculations:

Let the sum invested by P

⇒ 2188.68 = P + [(P × R × T)/100]

⇒ 2188.68 = P + [(P × 7 × 8)/100]

⇒ 2188.68 = P + (56P/100)

⇒ 2188.68 = 156P/100

⇒ P/100 = 14.03

⇒ P = Rs. 1403

∴ The sum of money is Rs. 1403

Given: 

The SI and CI for 2 years are 1200 and 1300 rupees respectively.

Concept: 

When SI for the first year is 'I' then CI for two years is 

CI = [I + I +( I × R%)]

Calculation: 

Let 'R' is the rate percent of per year 

Now, The simple interest for 1 year is 

⇒ 1200/2

⇒ 600 rupee

Now, The compound interest is 

⇒ 1300 = [600 + 600 + (600 × R%)]

⇒ 100 = 600 × R%

⇒ R% = 1/6

⇒ R = 16.66

So, The rate percent per half years is 

⇒ 16.66/2

⇒ 8.33

∴ The rate percent per half-year is 8.33 percent. 

Given:

Rate = 75%

Formula used:

For 2 years, CI – SI = P(r/100)²

for 3 years, CI – SI = P(r/100)² [(300 + r)/100]

Calculation

(CI – SI) for 2 years : (CI – SI) for 3 years = P(r/100)² : P(r/100)² (300 + r)/100

⇒ (CI – SI) for 2 years : (CI – SI) for 3 years = 100 : (300 + r)

⇒ (CI – SI) for 2 years : (CI – SI) for 3 years = 100 : (300 + 75)

⇒ (CI – SI) for 2 years : (CI – SI) for 3 years = 100 : 375 = 4 : 15

∴ Required ratio is 4 : 15

Given:

Principal = Rs. 2000

Rate of interest = 5%

Time = 3 years

Formula used:

Amount = Principal{1 + (rate/100)}^time

Calculation:

Amount = Principal{1 + (rate/100)}^time

⇒ 2000{1 + (5/100)}³

⇒ 2000(21/20)³

⇒ 2000 × (9261/8000)

⇒ 9261/4

⇒ 2315.25

∴ The amount will get after 3 years is Rs. 2315.25.

Given:

A = Rs. 2178

N = 2 Years

R₁ = 10% p.a.

R₂ = 5% p.a.

Formula used:

A = P × {1 + (R/100)}^N

Where P = Principal amount, R = Rate of interest in %, N = Number of years

Calculation:

According to formula,

2178 = P × {1 + (10/100)}²

⇒ 2178 = (P × 11 × 11)/100

⇒ P = (2178 × 100)/121

⇒ P = 1800

Now at 5% rate of interest

A = 1800 × {1 + (5/100)}²

⇒ A = (1800 × 21 × 21)/400

⇒ A = 1984.5

Given:

A = Rs. 6048 (after 2 years)

A = Rs. 7257.6 (After 3 years)

Formula used:

A = P × {1 + (R/100)}^N

Where, P = Principal, R = Rate of interest, N = Number of years

Calculation:

Let Amount after 3 years and 2 years be A3/A2 respectively.

Here, A₃/A₂ = 7257.6/6048

⇒ 7257.6/6048 = 1.20

A3/A2 = [P{1 + (R/100)}3]/[P{1 + (R/100)}2]

⇒ 1.20 = {1 + (R/100)}

⇒ 0.20 = R/100

⇒ R = 20%

Now, calculating P,

⇒ 6048 = P × {1 + (20/100)}²

⇒ 6048 = (P × 6 × 6)/(5 × 5)

⇒ P = Rs. 4200

∵ R decreased to 10%,

⇒ New rate of interest is (20 – 10) = 10%

A = 4200 × {1 + (10/100)}²

⇒ A = (4200 × 11 × 11)/(10 × 10)

⇒ A = 5082

Given:

Cost of the refrigerator = Rs.22, 800

Interest rate= 12.5 %

Amount paid at the end of the first year = Rs.8,650

Amount paid at the end of the second year = Rs.9,125

Calculation:

Cost of the refrigerator = Principal amount = Rs.22,800

Interest rate = 12.5%

After first year, interest = 12.5 % of Rs.22, 800 = Rs.2850

Principal amount remaining = Original Principal amount + Interest of first year - Amount  paid

⇒  22800 + 2850 - 8650

⇒  Rs.17000

After second year, interest = 12.5% of Rs.17,000 = Rs.2125

Principal amount remaining = Original Principal amount + Interest of second year - Amount  paid

⇒  17000 + 2125 - 9125

⇒  Rs. 10,000

After third year, interest = 12.5% of Rs.10,000 = Rs.1250

Amount to be paid too clear the debt = 10000 + 1250 = Rs.11,250

∴ Amount to be paid at the end of the third year is Rs.11, 250

Given:

Amount at the end of first year =  ₹ 650

Amount at the end of second year =  ₹ 676

Formula Used:

Amount = Pricipal(1 + Rate/100)^Time 

Calculation:

(Amount at the end of second year)/(Amount at the end of first year) = {principle × (1 + Rate/100)²}/{principle × (1 + Rate/100)}

⇒ (₹ 676)/(₹ 650) = (1 + Rate/100)

Principle = (Amount at the end of first year)/(1 + Rate/100)

⇒ Principle = (650)/{(676)/(650)}

⇒ Principle = (650)²/(676)

⇒ Principle = (422500)/(676)

⇒ Principle = ₹ 625

∴ The compound interest sum is ₹ 625.

Given :-

A sum of Rs. 10,500 amounts to Rs. 13,650 in 2 years at a certain rate percent per annum simple interest

compounded half yearly

Concept :-

Simple interest = (Principal × rate × time)/100

Simple interest = Amount - Principal

Compound interest = Amount - Principal 

Amount = Principal(1 + (r/100))^t

If interest is compounded half yearly then time become double and rate become half

Calculation :-

⇒ Simple interest = 13,650 - 10,500

⇒ Simple interest = Rs. 3150

⇒ 3150 = (10,500 × r × 2)/100

⇒ 3150 = 105 × r × 2

⇒ r = 3150/(105 × 2)

⇒ r = 15%

Now,

For compounded half yearly

⇒ Rate = (15/2)%

⇒ Time = 2 years

⇒ Amount = 10,500(1 + (15/200))²

⇒ Amount = 10,500(1 + (3/40))²

⇒ Amount = 10,500 × (43/40) × (43/40)

⇒ Amount = 12,134

∴ The sum will amount is 12,134