Simple and Compound Interest Quiz-1

Let the principal = x,  time = t years

Then interest = \frac{x}{4} , rate = r%

Now using the SI formula , we get

interest = \frac {principal \times rate \times time}{100}

\frac{x}{4}= \frac{x \times t \times t}{100}

t² = 25

t = 5%

Assuming Simple interest

P + \frac{P \times R \times 2}{100}  =  704.......(i)

P + \frac{P \times R \times 5}{100}  = 800.......(ii)

on solving (i) and (ii)

3PR/100 = 96

PR = 3200

P + \frac{P \times R \times 2}{100}  = 704

P  + \frac{3200 \times 2}{100} = 704

P  =  704 - 64 = 640

PR = 3200

640 R = 3200

R = 5 %

rate of interest per annum = 5 %

 

trebles → triples

Let principle = Rs 100

Rate = x

Time = 8 years

Amount = Rs 300 (as the principle triples)

Interest = 300 - 100 = 200 Rs

Interest = \frac{P \times R \times T}{100}

200 = \frac{100 \times x \times 8}{100}

R = \frac{200}{8} = 25%

Similarly, if it becomes 5 times, amount = 5 \times 100 = Rs 500

Interest = 500 - 100 = 400

400 = \frac{100 \times 25 \times time}{100}

time = \frac{400}{25} = 16 years

Alternate Method

Let the principle be 100 Rs

it trebles itself in 8 years, i.e, the amount becomes 300 Rs

Thus the principal from 100 Rs to amount to 300 Rs, i.e, increase in 2 units, it takes 8 years

Similarly, principal from 100 Rs to amount to 500 Rs, i.e, increase in 4 units, it takes 8 \times 2 = 16 years

 

Let the sum be Rs. 100

SI, for first four months = \frac{100 \times 20 \times 1}{100 \times 4} = Rs. 5

SI, for next four months = \frac{105 \times 20 \times 1}{100 \times 4} = Rs. 5.25

SI, for last four months = \frac{110.25 \times 20 \times 1}{100 \times 4} = Rs. 5.5125

Amount at the end of 1 year = 100 + 5 + 5.25 + 5.5125 = 115.76

Effective rate = 115.76 - 100 = 15.76 %

C.I when interest compounded yearly

= Rs [8050 \times (1 + \frac{8}{100}) \times (1 + \frac{\frac{1}{2} \times 8}{100})]

= Rs [8050 \times \frac{27}{25} \times \frac{26}{25}]

= Rs 8052.12

C.I when interest compounded half - yearly

= Rs[8050 \times (1 + \frac{4}{100})^{3}]

= Rs[8050 \times \frac{26}{25} \times \frac{26}{25} \times \frac{26}{25}]

= Rs 9055.16

Difference = Rs (9055.16 - 8052.12) = Rs 1003.04

P=Rs.3300

A=Rs.3399

R=6%per annum

Let the time be n years.

Compound interest is taken half - yearly.

A = P [1 + (\frac{\frac{R}{2}}{100})]^{2n}

3399 = 3000 [1 + (\frac{\frac{6}{2}}{100})]^{2n}

\frac{3399}{3000} = [1 + (\frac{3}{100})]^{2n}

1.03 = [\frac{103}{100}]^{2n}

1.03 = [1.03]^{2n}

Thus, 1 = 2n

n = \frac{1}{2} = 6 months

Let Principle = x, Rate = r

According to the question

\frac{x \times (r+4) \times 4}{100} - \frac{x \times r \times 4}{100} = 120

\frac{x \times (r+4)}{25} - \frac{x \times r}{25} = 120

\frac{xr + 4x - xr}{25} = 120

x = 750 Rs

 

 

Let P = Rs 100,

A =  100 + 50% of 100 = 150

SI = 150 - 100 = 50 Rs

=> R = \frac{100 \times 50}{100 \times 5} = 10%

For CI, P = 20,000

CI = Rs [20000 \times {((1 + \frac{10}{100})^{4} - 1)}]

CI = Rs [20000 \times \frac{4641}{10000}]  = Rs 9282

 

 

For calculating the compound interest we have to first calculate the amount

formula -

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

A = 10000 (1 + \frac{8}{100})^{4}

A= 18,106.39 Rs

CI = A - P

= 18,106.39 - 10,000

= 8106.39