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Given:

S.I. on certain sum of money at 5% p.a. for 4 years is Rs. 1,750.

Concepts used:

S.I. = P × R × T/100

C.I. = P × [1 + (R/100)]^T – P

Calculation:

S.I. = P × R × T/100

⇒ Rs. 1,750 = P × 5 × 4/100

⇒ P = Rs. 1,750 × 100/5 × 4 

⇒ P = Rs. 8,750

C.I. = P × [1 + (R/100)]T – P

⇒ Rs. 8,750 × [1 + (5/100)]4 – Rs. 8,750

⇒ Rs. 10,635.68 – Rs. 8,750

⇒ Rs. 1,885.68

∴ C.I. for 4 years at 5% p.a. on principal amount being, Rs. 8,750 is Rs. 1,885.68.

Given:     

SI rate of interest = 15%

CI rate of interest = 10%

Difference between compound interest and simple interest for two years = Rs. 480.

Formula Used:

Simple Interest = (P × R × T)/100    

Compound Interest = P(1 + R/100)^T – P  

Where,

P → Principal 

R → Rate of interest 

T → Time 

Calculations:

Let the total principal be x

Simple Interest in two years = ((x/3) × 15 × 2)/100 = x/10

Compond Interest in two years = (2x/3)(1 + 10/100)² – 2x/3

⇒ (2x/3) × 121/100 – 2x/3

⇒ (121x/150) – 2x/3

⇒ 21x/150

According to the querstion,

⇒ (21x/150) – (x/10) = 480

⇒ 6x/150 = 480

⇒ x = 12000

∴ The total amount invested was Rs. 12000

Given:

The sum of amounts of A and B at the end of 4 years and 2 years respectively on the same principal = Rs. 20,020

Concept used:

1.) S.I. = (P × T × R)/100

2.) A = P + S.I.

3.) A = P(1 + R/100)^T

Where,

S.I. → Simple interest

A → Amount

P → Principal

T → Time

R → Rate

Calculations:

Let the principal be x

According to the question

\(\Rightarrow {\rm{}}\left( {{\rm{x}} + {\rm{}}\frac{{{\rm{x\;}} \times {\rm{\;}}4{\rm{\;}} \times {\rm{\;}}10}}{{100{\rm{\;}}}}} \right){\rm{}} + {\rm{x}}{\left( {1{\rm{}} + {\rm{}}\frac{5}{{100}}} \right)^2}{\rm{}} = {\rm{}}20,020\)

⇒ 7x/5 + x(441/400) = 20,020

⇒ (560x + 441x)/400 = 20,020

⇒ 1001x/400 = 20,020

⇒ x = 8000

∴ The principal is Rs. 8,000

Given:

Principal (P) = 21630,

Rate (R) = 20/3%,

Installment = 3

Formula used:

Instalment = \(\frac{x}{{{{(1 + \frac{R}{{100}})}^n}}}\)

Calculation:

Let, x be the equal instalment

Total number of instalment is 3

Accordingly,

 \(\frac{x}{{1 + \frac{{20}}{{300}}}} + \frac{x}{{{{(1 + \frac{{20}}{{300}})}^2}}} + \frac{x}{{{{(1 + \frac{{20}}{{300}})}^3}}} = 21630\)

⇒ \(\frac{{15x}}{{16}} + \frac{{225x}}{{256}} + \frac{{3375x}}{{4096}} = 21630\)

⇒ (3840x + 3600x + 3375x) = 4096 × 21630

⇒ 10815x = 4096 × 21630

⇒ x = (4096 × 21630)/10815

∴ Installment is 8192

Given:

Actual price = Rs. 1680

Down payment = Rs. 400

Formula used:

Simple Interest = PRT/100

Calculation:

Total amount = Rs. (1400 + 287) = Rs. 1687

Interest paid = Rs. (1687 – 1680)

⇒ Rs. 7

Interest will be applied on = Rs. (1680 – 1400) = Rs. 280

Simple Interest = PRT/100

⇒ 7 = (280 × R × 1)/100

⇒ R = 700/280

⇒ R = 2.5% per month

⇒ R = 2.5 × 12

⇒ R = 30% per annum

∴ Rate of simple interest charged is 30% per annum.

Given:

Principal = Rs. 33,000

Time = 3 years

Rate = 10% per annum at SI

Formula used:

A = nx + {(n – 1) + (n – 2) +(n – 3) + …}Rx/100

where A = Total amount paid

x = value of each instalment

n = time for instalment

R = Rate (%)

Calculations:

SI = (33000 × 10 × 3)/100

⇒ Rs. 9900

A = Rs. (33,000 + 9900)

⇒ Rs. 42,900

42900 = 3x + {(3 – 1) + (3 – 2)}10x/100

⇒ 42900 = 3x + {(2 + 1 )10x}/100

⇒ 42900 = 3x + (30x/100)

⇒ 42900 = 330x/100

⇒ 42900/330 = x/100

⇒ 130 = x/100

⇒ 13000 = x

∴ Annual instalment is Rs. 13,000

Given:

Principal = Rs. 16,550

Rate = 10% per annum

Time = 3 years

Formula used:

For Installment at CI,

P = x/{1 + (R/100)} + x/{1 + (R/100)}² + x/{1 + (R/100)}³ + …

where,

P = Money borrowed or Principal.

x = value of each instalment

R = Rate (%)

Calculation:

Let value of one instalment be x.

x/{1 + (R/100)} + x/{1 + (R/100)}² + x/{1 + (R/100)}³ = 16550

⇒ x/{1 + 10/100) + x/(1 + 10/100)² + x/(1 + 10/100)³ = 16550

⇒ x/(1 + 1/10) + x/(1 + 1/10)² + x/(1 + 1/10)³ = 16550

⇒ x/(11/10) + x/(11/10)² + x/(11/10)³ = 16550

⇒ 10x/11 + 100x/121 + 1000x/1331 = 16550

⇒ (1210x + 1100x + 1000x)/1331 = 16550

⇒ 3310x/1331 = 16550

⇒ x = Rs. 6655

∴ Annual installment is Rs. 6655

Given:

(i) Two annual instalments = Rs. 2646

(ii) Rate (R) = 5% pa CI

Calculations:

According to the question,

Principal = [2646/(1 + 5/100) + 2646/(1 + 5/100)²]

⇒ (2646 × 20)/21 + (2646 × 400)/441

⇒ 126 × 20 + 6 × 400

⇒ 2520 + 2400

⇒ 4920.

The amount borrowed by Miku was Rs. 4920.

Given:

The principal is Rs. 1275

Rate of interest is 4 %

Number of installment is 2.

Formula used:

P( 1+ R/100)ⁿ = X( 1+ R/100)^n-1  +  X( 1+ R/100)^n-2  + X( 1+ R/100)^{n -3} +  X( 1+ R/100)^n-4 + ----

Where,

P = principal

R = Rate       

n = number of installments

X = amount of installment

Calculation:

Let the value of installment be Rs. X

⇒ 1275(1 + 4/100)² = X(1 + 4/100)^2-1

⇒ 1275 × 104/100 × 104/100 = (X + 104 X/100)

⇒ 1275 × 104/100 × 104/100 = 204 X/100

⇒ X = 676

∴ The value of installment is Rs. 676.

Given:

Principal = Rs. 20000, Rate = 15%, Time = \(2\frac{2}{{3\;}}\;{\rm{years}}\)

Formula used:

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

Calculation:

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

\(\Rightarrow 20000 \times {\left( {1 + \;\frac{{15}}{{100}}} \right)^2}\left( {1 + \;\frac{{\frac{2}{3} \times 15}}{{100}}} \right)\)

\(\Rightarrow 20000 \times {\left( {\;\frac{{23}}{{20}}} \right)^2}\left( {\;\frac{{11}}{{10}}} \right)\)

⇒ 5 × 23 × 23 × 11

⇒ 29095

Interest = Amount – Principal

⇒ 29095 – 20000

⇒ 9095

∴ The compound interest is Rs. 9095.

Given:

Diksha invested Rs 70,000 at the rate of 18% compounded annually for 2 years.

Shreya invested Rs 76,000 under simple interest at the rate of 9% per annum for 4 years.

Formula Used:

Simple Interest = P × r × t/100

Compound Interest = P[1 + (r/100)^t – 1]

Where,

P → Principal

r → Rate of interest

t → Time

Calculation:

Compound Interest of Diksha = P[(1 + r/100)^t – 1]

⇒ 70,000[(1 + 18/100)² – 1]

⇒ 70,000 × [(118/100)² – 1]

⇒ 70,000 × 1.18 × 1.18 – 70,000

⇒ 97,468 – 70,000

⇒ Rs. 27,468

Simple Interest of Shreya = P × r × t/100

⇒ (76,000 × 9 × 4)/100

⇒ Rs 27,360

Difference between the interest of Diksha and Shreya = 27468 – 27360

⇒ Rs 108

∴ The difference between the interest of Diksha and Shreya is Rs 108.

Given:

Amount lent by Ishwar from Abdul (Principal) = Rs.2400

Number of years = 3

Rate of Interest for the first year = 2%

Rate of Interest for the second year = 4%

Rate of Interest for the third year = 6%

Formula Used:

When the rates of Interest are R₁%, R2%, and R₃% for the first, the second and the third year, respectively; then the amount at the end of three years is given as:

Amount = P × [1 + (R₁/100)] × [1 + (R₂/100)] × [1 + (R₃/100)]

Interest = Amount - Principal

Calculation:

The amount will be calculated according to the above-mentioned formula, as:

Amount = 2400 × [1 + (2/100)] × [1 + (4/100)] × [1 + (6/100)]

⇒ Amount = 2400 × 1.02 × 1.04 × 1.06 

⇒ Amount = Rs.2698.68

∵ Compound Interest = Amount - Principal

∴ The compound Interest is calculated as:

2698.68 - 2400 =  Rs.298.68

∴  The additional money that Ishwar needs to pay at the end of three years, in the form of compound interest, is Rs.298.68

Given:

Loan taken from the bank by Soumya and Mangal, each = Rs.4000 

The time period to repay the loan for both = 2 years

Rate of Interest Compounded Quarterly for Soumya = 15%

Rate of Interest Compounded Annually for Mangal = 20%

Formulae Used:

If P = Principal,

R= Rate of Interest, and 

n = number of years, then:

When the interest is compounded annually,

Amount = P [1 + (R/100)]ⁿ

When the interest is compounded quarterly,

Amount = P [1 + (0.25R/100)]4n

Calculation:

The amount needed to be repaid by Soumya at the end of two years is given by:

4000 × {1 + [(0.25 × 15)/100]}⁸ = 4000 × [1 + (3.75/100)]8

⇒ 4000 × (1.0375)8 = Rs.5369.88

The amount needed to be repaid by Mangal at the end of two years is given by:

4000 × [1 + (20/100)]² = 4000 × (1.2)²

⇒ 4000 × 1.44= Rs.5760

∴ The difference in the amount to be repaid by Soumya and Mangal at the end of two years is given by:

5760 - 5369.88 = 390.12

∴ The difference in the amount needed to be repaid by Soumya and Mangal after two years is Rs.390.12

Given:

A sum of Rs. 4400 is to be divided among three NGOs in such a way that simple interest for each at 8% annum after 2 , 4 , 6 years respectively will be same .

Formula used:

Simple Interest = {Sum (P) × rate of interest (r) × time (t)}/100

Calculation:

Let the sum of 1st, 2nd and 3rd NGO be P_{1 ,} P₂ and P₃ respectively.

S.I of 1st NGO = (P₁ × 8 × 2)/100

S.I of 2nd NGO = (P₂ × 8 × 4)/100

S.I of 3rd NGO = (P₃ × 8 × 6)/100

According to the question,

(S.I)_1st = (S.I)_2nd = (S.I)_3rd

⇒ 2P₁ = 4P₂ = 6P₃

⇒ P₁ : P₂ : P₃ = 24 : 12 : 8 = 6 : 3 : 2

Share of 1st NGO = Rs. (4400 × 6/11) = 2400

Share of 3rd NGO = Rs. (4400 × 2/11) = 800

Difference between the share of first and third NGO = Rs. (2400 – 800) = Rs. 1600

Given:

Principal = Rs. 2100

Rate of interest = 8%

Time period = 2 years and 3 years

Concept used:

S.I for each and every year is the same. So, the difference will be interest for 1 year

S.I = PRT/100

Calculation:

S.I for 1 year = Rs. (2100 × 8)/100

⇒ Rs. 168

∴ The required difference is Rs. 168

Given:

Amount = Rs. 8680

Principal = Rs. 7000

Rate = 4% per annum

Formula used:

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

Simple interest = Amount – principal

Calculation:

Simple interest = Rs.(8680 - 7000)

⇒ Rs. 1680

Time = (1680 × 100)/(7000 × 4)

⇒ 6 years

Concept used:

SI = PRT/100

Amount = Principal + Interest

Calculations:

We know that,

SI = (PRT/100)

⇒ SI = (4000 × 20 × 3)/100

⇒ SI = 2400

Amount = Principal + Interest

⇒ A = 4000 + 2400 = 6400

∴ Required amount is Rs. 6400

Given:

Principal(P) = Rs. 7000

Rate of interest(R) = 20% per annum

Simple interest = Rs. 1750

Formula used:

Simple interest(SI) = \(\dfrac{P \times R \times T}{100}\)

Calculation:

According to the question:

1750 = \(\dfrac{7000 \times 20 \times T}{100}\)

⇒ T = 175000/140000

⇒ T = 1.25 years = 15 months

∴ Amount was invested for 15 months

Given:

The compound interest on an amount invested for 2 years at 12% per annum is Rs. 2544.

Formula:

CI = P [1 + (r/100)]ⁿ – P, when the rate of interest is r and the amount is invested for n years.

SI = PRT/100

Calculation:

Let the sum be Rs. P.

2544 = P [1 + (12/100)]² – P

P = 10000

Now, simple interest on Rs. 10,000

SI = (10000 × 7 × 8)/100

⇒ Rs. 5600

∴ The simple interest is Rs. 5600

Given:

Mr. X invests Rs 5500 for 3 years at 8% p.a

compound interest reckoned yearly.

 Income tax at the rate of 15% on the interest earned

is deducted at the end of each year.

Formula Used:

CI = P [1+(R/100)]n - P

Calculation:

ATQ,

The interest earned at the end

of first year will be -

CI = 5500(1.08)¹ – 5500

CI = Rs.440

Income tax @15% is deducted on the Interest earned =440 × (3/20) = 66

Amount at the end of first year = 5500 + 440 – 66 = 5874

Now the amount at the end of first year is taken as principal at the beginning of second year

Interest earned at the end of second year CI = 5874(1.08) – 5874 = 469.92

Income tax deducted = 469.92 × ((3/20) = 70.488

Amount at the end of second year =  5874 + 469.92 - 70.488 = 6273.432

Interest earned at the end of third year CI = 6273.432(1.08) – 6273.432 = 501.874

Income tax deducted = 501.874 × (3/20) 

⇒ 75.28

Amount at the end of third year = 6273.432 + 501.874 – 75.28

⇒ 6700.0026 ≈ 6700

∴ The amount at the end of third year is Rs. 6700

Given:

The amount received = Rs. 9984

Formula used:

SI = (P × R × T)/100

Total amount = P(1 + x/100)^t

Calculation:

Let the Sum be the x

⇒ 130/100 × x = 9984

⇒ x = (9984 × 100)/130

⇒ x =  Rs. 7680

SI = (P × R × T)/100

S.I = (7680 × 15 × 2)/100

⇒ S.I = Rs. 2304

According to question

C.I = 2304 + 6500

⇒  Rs. 8804

Total amount = 7680 + 8804

Total amount = P(1 + x/100)t

⇒ 16484 = 7680(1 + x/100)²

⇒ (1 + x/100)2  = 16484/7680

⇒ 1 + x/100 = √2.1463 

⇒ x/100 = 1.465 – 1

⇒ x = 46.5%

∴ The value of x is 46.5%

Given:

Principle = 10,000 Rs.

Amount = 15,840 Rs.

Formula used:

Amount = Simple Interest + Principal

SI = (P x R x T)/100,

where P = Principal,

R = Rate of Interest,

T = Time Period of the Loan/deposit in years,

SI = Simple Interest

Calculations:

⇒ SI = 15,840 - 10,000

⇒ SI = 5840

⇒ 5840 = (1000 × 4 × r)/100

⇒ r = 14.6%

∴ The rate of interest is 14.6%.

Given:

A sum of Rs. 23000 was invested under simple interest for 8 years at a rate of interest 8%.

A sum of Rs. 95000 was invested under compound interest at a rate of 12% for two years.

Formula Used:

Simple Interest = Principal × rate × time/100 = prt/100 (Where principal be p and rate be r).

Interest under compound interest = p × [(1 + r/100)ⁿ – 1]

Calculation:

Interest under compound interest = 95000[(1 + 12/100)² – 1]

⇒ 95000 × 1.12 × 1.12 – 95000 = Rs. (119168 – 95000) = Rs. 24168

Interest under SI = prt/100 = Rs. (23000 × 8 × 8/100) = Rs. 14720

Difference = Rs. (24168 – 14720) = Rs. 9448

Given:

The compound interest on an amount invested for 2 years at 15% per annum is Rs. 387.

Formula Used:

CI = P × (1 + r/100)ⁿ – P, where the rate of interest is r and the amount P is invested for n years.

SI = principal × rate × time/100 = Prt/100

Calculation:

Let the sum be Rs. P.

⇒ 387 = P (1 + 15/100)² – P

⇒ P = 1200

Now SI for 4 years at 5% simple interest rate = 1200 × 4 × 5/100 = 240 (in Rs.)

∴ Required simple interest is Rs. 240

Given:

The simple interest on an amount invested at 13% per annum for 9 years is five times of the compound interest on Rs. 18000 for 2 years at 17% per annum

Formula Used:

CI = P × (1 + r/100)ⁿ – P, where the rate of interest is r and the amount is invested for n years.

SI = principal × rate × time/100 = Prt/100

Calculation:

S.I. = P × 13 × 9/100 = 117P/100

CI = Rs. {18000 × (1 + 17/100)² – 18000} = Rs. (24640.2 – 18000) = Rs. 6640.2

⇒ 117P/100 = 5 × 6640.2 = 33201

⇒ P = 28377

∴ The invested amount was Rs. 28377

Given:

Time period = 10 years

Formula used:

\(\rm S.I = \frac{{{\rm{P\;}} × {\rm{\;t\;}} × {\rm{\;r}}}}{100}\)

P = principal

t = Time period

r = Rate of interest

Calculation:

Let P be Rs. x

According to the question,

According to the question money becomes 5x

So, interest = 5x – x = 4x

\(\rm 4x = \frac{{{\rm{x\;}} × {\rm{\;10\;}} × {\rm{\;r}}}}{100}\)

⇒ 400x = 10xr

⇒ 40 = r

⇒ Rate of interest = 40%

∴ Required rate of interest is 40%

Given:

P = 10,000

T = 3 years

R = 10%

Formula Used:-

Difference = (Sum × (Rate)²) × (300 + rate)/100³

Calculation:

Here, P = 10,000, R = 10%, T = 3 years

⇒ Difference = (10,000 × 100 × 310)/1000000

Given:

Rate = \(12 \dfrac{2}{4}\%\) = (50/4)%

Formula:

SI = Prt/100

Calculation:

Let principal be Rs. x, then

SI = Rs. x

According to the question

x = (x × 50 × t)/(100 × 4)

⇒ t = 8 years 

∴ In 8 years will the simple interest be equal to the principal.

Given:

Amount after 4 years = Rs. 504

Amount after 7 years = Rs. 582

Formula used:

S.I. = (P × R × T)/100

Where, S.I. → Simple Interest

P → Principal

R → Rate 

T → Time 

Calculations:

S.I. for 3 years = Rs. (582 – 504) = Rs. 78

So, S.I. for 1 year = Rs. 78/3 = Rs. 26

Again, S.I. for 4 years = Rs. 26 × 4 = Rs. 104

Thus, Principal = Rs. (504 – 104) = Rs. 400

So, R = (100 × 104)/(400 × 4) = 6.5%

∴ The rate % p.a is 6.5%.

Given:

P = Rs. 2560

R = 25% p.a.

Formula used:

Difference = P × (R/100)²

Calculation:

According to given

⇒ Difference = 2560 × (25/100)²

⇒ Difference = 160

 ∴ required difference is Rs. 160

Given:

Amount = Rs. 6300

Time = 2 years

Rate of Interest = 10%

Formula Used:

Installment = \(\frac{100\ \times \ A}{100 \ \times \ t \ + \ R\ \times \ t(\frac{t \ - \ 1}{2})}\)

Where, A = Amount

t = Time

R = Rate of Interest

Calculation:

Installment = \(\frac{100\ \times \ A}{100 \ \times \ t \ + \ R\ \times \ t(\frac{t \ - \ 1}{2})}\)

⇒ \(\frac{100\ \times \ 6300}{100 \ \times \ 2 \ +\ 10 \ \times \ 2(\frac{2 \ - \ 1}{2})}\)

⇒ \(\frac{630000}{200 \ + \ \frac{20}{2}}\)

⇒ 630000/210 = 3000

Given:

Loan Amount(P) = Rs. 10,000

Time = 3 years

Rate for 1^st year(x) = 10%

Rate for 2^nd and 3^rd year(y) = 15%

Formula used:

Net effect formula for CI = x + y + (x × y) / 100

Calculations:

Rate for 1^st, 2^nd and 3^rd year is 10%,15% and 15%

P = 10,000 and T = 3 years

Net effect for 1^st 2 years

⇒ x + y + (x × y) / 100

⇒ 10 + 15 + (10 × 15) / 100

⇒ 26.5%

Now for 3^rd year

⇒ 26.6 + 15 + (26.5 × 15) /100

⇒ 41.5 + 3.975

⇒ 45.475%

Let, Principal be 100x

Amount = (P + CI)

= 100x + 45.475x

⇒ 145.475x

⇒ 100x = 10000

⇒ 145.475x = 14547.5

∴The amount Aman will have to pay is Rs. 14547.5. 

Given:

Principal (P) = Rs.9,000, Time (T) = 2 years, Rate (R) = 7%

Formula used:

The difference between S.I. and C.I. for 2 years = PR²/(100)²

Where P → Principal

R → Rate

Calculations:

According to the question,

The required difference = (9000 × 7 × 7)/(100)²

⇒ Rs.44.10

∴ The difference between S.I. and C.I. for 2 years is Rs.44.10.

Given:

C.I. - S.I. = Rs.702      ----(i)

Rate (R) = 12%

Time (T) = 3 years

Formula used:

S.I. = (P × R × T)/100 

A = P(1 + R/100)n

Where A → amount

n → time

S.I. → Simple Interest

P → Principal

R → Rate 

T → Time

Calculations:

Let the sum of money be Rs. P.

According to the question,

S.I. = (P × 12 × 3)/100 = 9P/25      ----(ii)

Similarly, C.I. = P(1 + 12/100)³ - P

⇒ C.I. = P × (28/25) × (28/25) × (28/25) - P

⇒ C.I. = (21952P/15625) - P

⇒ C.I. = (6327P/15625)      ----(iii)

Putting values of C.I. and S.I. from (iii) and (ii) respectively in (i),

We get, (6327P/15625) - (9P/25) = 702

⇒ {(6327P - 5625P)/15625} = 702

⇒ (702P/15625) = 702

⇒ P = Rs.15625

∴ The principal is Rs.15625.

Given:

Time (T) = 2 years

Time (n) = 3 years

Formula used:

S.I. = (P × R × T)/100 

A = P(1 + R/100)n

Where A → amount

n → time

S.I. → Simple Interest

P → Principal

R → Rate 

T → Time

Calculations:

Let the principal be Rs. P and the rate be R p.a.

The principal after 2 years = P + 14P/100

According to the question,

P + 14P/100 = P + (P × R × 2)/100

⇒ 1 + (14/100) = R/50

⇒ R = 50 × (14/100) = 7%

Now

A = 10000(1 + 7/100)³

⇒ A = 10000 × (107/100) × (107/100) × (107/100)

⇒ A = Rs.12250.43

Thus C.I. = 12250.43 - 10000 = Rs.2250.43

∴ The compound interest earned on Rs10,000 in 3 years is Rs.2250.43.

Given:

Rate = 15 %

Difference between CI and SI in 2 years= Rs. 3375

Time = 2 years

Concept:

CI – SI = P × (R/100)²

Calculation:

⇒ 3375 = P × (15/100)²

⇒ P = 150000

∴ The required result will be 150,000

Given:

Sum = Rs.400

Amount = Rs.441 

Time = 2 years

Formula Used:

For compound interest,

A = P(1 + R/100)ⁿ

where,

A = Amount 

P = Sum

R = Rate of interest

n = Number of years

Calculation:

A = P(1 + R/100)n

⇒ 441 = 400(1 + R/100)²

⇒ 441/400 = (1 + R/100)2

⇒ √(441/400) = 1 + R/100

⇒ 21/20 = (100 + R)/100

⇒ 21 = (100 + R)/5

⇒ 105 = 100 + R

⇒ R = 105 – 100

⇒ R = 5%

Now the rate of interest increased by 5%

⇒ Total rate of interest = 5% + 5%

⇒ Total rate of interest = 10%

A = P(1 + R/100)n

⇒ A = 400 (1 + 10/100)²

⇒ A = 400 (1 + 1/10)²

⇒ A = 400 (11/10)²

⇒ A = 400 × 11/10 × 11/10

⇒ A = 4 × 11 × 11

⇒ A = 484

∴ Amount received is Rs.484

Given:

Sum = Rs. 37,500

Time = 2 years

Rate = 12% at compound interest

Formula:

Interest after n years under compound interest = P × [1 + (r/100)]ⁿ - P

Calculation:

C.I after 2 years = 37500 [1 + (12/100)]² – 37500

⇒ 47040 – 37500 = 9540

Let the time be t

Interest under SI = Rs. (9540 + 2460) = Rs. 12,000

⇒ (37500 × t × 8)/100 = 12000

T = 4 years

∴ The required time is 4 years

GIVEN:

The simple interest on a sum of money is half of the sum invested.

FORMULA USED:

SI = (P × R × T)/100

CALCULATION:

Suppose time = R/2, Rate = R

Now,

P/2 = (P × R × R)/(100 × 2)

⇒ R² = 100

⇒ R = 10%

∴ The rate percentage per annum is 10%

Given:

Rate of interest = 12%

time = 3.5 years

Formula used:

Simple interest = (principal amount × rate of interest × time)/100

Calculation:

Let P be the principal amount

So, S.I. = 994 – P

⇒ 994 – P = (P × 12 × 3.5)/100

⇒ 99400 – 100P = 42P

⇒ 142P = 99400

⇒ P = 700 Rs

∴ The principal amount invested was Rs. 700.

Given:

 A certain amount of money was invested for certain time and at a certain rate under simple interest. After 2 years, amount became Rs. 24000 and after 5 years, total amount was Rs. 30000.

Formula:

Amount under simple interest = P × r × t/100,

where P is principal,

r is rate of interest,

and t is time

Amount under compound interest = P + (P × r × t/100)

Calculation:

 P + 2I = 24000, where I is interest

and P+5I = 30000

Solving above equations, we get

3I = 6000

⇒ I = 2000 

Principal= Rs 20000

Given:

A sum of money, when invested at a certain rate of compound interest per year, became 1.21 times

The sum invested on maturity after two years

Formula used:

Compound interest (A) = Principal amount × [1 + (rate of interest/100)]^t

Calculation:

Principal amount = p

Amount = 1.21P

Time = 2 year

Rate of interest = r

⇒ 1.21P = P [1 + (r/100)]²

⇒ 1.21 = [1 + (r/100)]²

⇒ (1.1)² = [1 + (r/100)]²

⇒ 1.1 = (100 + r)/100

⇒ 110 = 100 + r

⇒ r = 10%

∴The rate of compound interest per annum is 10%

Given:

Principal = Rs. 40000

Rate% = 12.5%

Time = 2 years

Formula used:

\(CI = P × \left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^n}-1} \right]\)

Calculation:

\(CI = P × \left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^n}-1} \right]\)

\(⇒ CI = 40000 × \left[ { {{\left( {1 + \frac{12.5}{{100}}} \right)}^2}-1} \right]\)

⇒ CI = 40000 × [(1 + 1/8)² – 1 ]

⇒ CI = 40000 × (81/64 – 1)

⇒ CI = 40000 × (17/64)

∴ CI is Rs. 10625

Given:

Simple Interest = Rs. 2880

Rate % = 8% p.a

Time = 9 years

Formula used:

Simple Interest = P × r/100 × t

Where P = principal,

r = rate %

t = time

Calculation:

Simple interest = P × r/100 × t

⇒ 2880 = P × 8/100 × 9

⇒ P = 2880 × 100/72

⇒ P = Rs. 4000

According to the question, rate for 6 years for  same interest can be found as

⇒ Simple interest = 4000 × r/100 × 6

⇒ 2880 = 4000 × r/100 × 6

⇒ r = 2880/240

⇒ r = 12%

∴ The required rate percent is 12% 

Given:

Principal = Rs 6,535

Rate of interest = 10%

Time in years = 6 years

Concept used:

Simple interest, SI = (P × N × R)/100

Where P is principal, N is the number of terms and R is the rate of interest.

Calculation:

SI = 6535 × 6 × 10/100 = Rs 3,921

∴ The simple interest obtained is Rs 3,921.

Given:

P₁ : A₁ = 2 : 3

After 4 years = P₁ : A₂ = 5 : 8

Formula used:

I = PRN / 100

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

Calculation:

Here, principal amount remains the same and rate of simple interest also remains same.

⇒ 2 : 3 = 1 (Difference)

⇒ 5 : 8 = 3 (Difference)

Now, 2 part and 5 part is principal amount which is same so equating principal amount

⇒ 10 : 15 = 5----(1)

⇒ 10 : 16 = 6   ----(2)

Equation 1 shows interest obtained after fixed period of time and equation 2 shows interest obtained after 4 years from interest 1

⇒ Interest in 4 years = (6 – 5) units

⇒ Interest in 4 years = 1 unit

⇒ Interest in 1 years = 1/4 units

Placing it in formula,

⇒ 1 / 4 = 10 × R × 1 / 100  [Let, principal is 10 unit and time is 1year]

⇒ R = 100 / (10 × 4)

⇒ R = 2.5%

Given:

A = 3 × P

R = 12.5%

Formula used:

I = PRN / 100

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

A = P + I    

Where A = Amount received

Calculation:

Let principal amount be X, A = 3X

⇒ I = 3X – X

⇒ I = 2X

Accordingly,

2X = (X × 12.5 × N / 100)

⇒ 2 = 25 × N / 200

⇒ N = 400 / 25

⇒ N = 16 years

Given:

P₁ = Rs. 1000, N₁ = 2 Years

P₂ = Rs. 1350, N₂ = 5 Years

P₃ = Rs. 1450, N₃ = 7 Years

P₄ = Rs. 1500, N₄ = 8 Years

Formula used:

I = PRN / 100

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

Calculation:

Here Total Interest = (P₁R₁N₁ / 100) + (P₂R₂N₂ / 100) + (P₃R₃N₃ / 100) + (P₄R₄N₄ / 100)

⇒ (1000 × 2 × R/100) + (1350 × 5 × R / 100) + (1450 × 7 × R / 100) + (1500 × 8 × R / 100) = 2472

⇒ 20R + 67.5R + 101.5R + 120R = 2472

⇒ 309R = 2472

⇒ R = 8

Given-   

Rate = 15%

Time = 3 years

Interest = Rs. 1350

Formula Used-

Interest = P × R × T/100    [where P = Principal, R = Rate, T = Time]

Calculation- 

Let P = Principal, R = Rate, T = Time

According to Question-

P × 15 × 3/100 = 1350

⇒ P = 3000

∴ Simple interest for next 2.5 years = 3000 × 15 × 2.5/100

⇒ Rs. 1125  

Given:

Amount = Rs. 10920

Rate of interest = 10%

Time = 4 years

Formula used:

SI = P × R% × T

where, P = Principal, R = Rate of interest, T = Time 

Amount = P + SI

Calculation:

Let the principal sum be Rs. P.

Amount = Principal + SI

⇒ 10920 = P + P × R% × T

⇒ 10920 = P(1 + 10/100 × 4)

⇒ 10920 = P(1 + 2/5)

⇒ 10920 = 7P/5

⇒ P = Rs. 7800

∴ The sum of money he borrowed is Rs. 7800.