In what time will 8000 amount to 8820 at 10% pa interest compounded half yearly?

Chapter 13: SIMPLE INTEREST

Introduction

• Relation Among Principal, Time, Rate Percent of Interest Per Annum and Total Interest :

  Nội dung chính Show

  • Chapter 13: SIMPLE INTEREST
  • Introduction
  • Compound Interest
  • Solved Problems
  • CAT Problems
  • In what time will ₹ 800 amount to ₹ 882 at 10% per annum compounded half yearly?
  • In what time will rupees 1800 amount to rupees 882 at 5% per annum compounded annually?
  • At what time will rupees 8000 amount to 8820 at 5% per annum compounded annually?
  • At what rate of compound interest will Rs 1250 amount to Rs 1800 in 2 years 2 points?
  • In what time will 8000 amount to 8820 at 5% pa interest compounded half yearly?
  • In what time will Rs 8000 amounts to Rs 8820 at 10% per annum if interest being compounded half yearly?
  • What is the compound interest on 8000 at 10%?
  • What is the compound interest on 8000 at 10% pa for 2 years if the interest is?

  Nội dung chính Show

  • Chapter 13: SIMPLE INTEREST
  • Introduction
  • Compound Interest
  • Solved Problems
  • CAT Problems
  • In what time will ₹ 800 amount to ₹ 882 at 10% per annum compounded half yearly?
  • In what time will rupees 1800 amount to rupees 882 at 5% per annum compounded annually?
  • At what time will rupees 8000 amount to 8820 at 5% per annum compounded annually?
  • At what rate of compound interest will Rs 1250 amount to Rs 1800 in 2 years 2 points?




• Amount = Principal + Total interest




• A = P + \( \frac{P * t * r}{100} \)




• Time = \( \frac{\text{Total interest}}{\text{Interest on the principal in one year}} \). Thus, if we have the total interest as ` 300 and the interest per year is ` 50, then we can say that the number of years is 300/50 = 6 years.

COMPOUND INTEREST

• Let principal = P, time = n years and rate = r% per annum and let A be the total amount at the end of n years, then A = P[\( 1 + \frac{r}{100} \)]n




• When compound interest is reckoned half-yearly. If the annual rate is r% per annum and is to be calculated for n years. Then in this case, rate = (r/2)% half-yearly and time = (2n) half-years then A = P[\( 1 + \frac{r/2}{100} \)]2n




• When compound interest is reckoned quarterly. In this case, rate = (r/4)% quarterly and time = (4n) quarter years. \ As before, then A = P[\( 1 + \frac{r/4}{100} \)]4n




• The difference between the compound interest and the simple interest over two years is given by \( \frac{P * r^2}{100^2} \)

Q.

The SI on a sum of money is 25% of the principal, and the rate per annum is equal to the number of years. Find the rate percent.

4.5

6

5

8

Ans .

5 

1. Explanation :

   Let principal = x, time = t years
   Then interest = x/4, rate = t%
   Now, using the SI formula, we get
   Interest = (Principal × Rate × Time)/100
   so x/4 = (x × t × t)/100
   so t2 = 25
   and we get t = 5%

Q.

The rate of interest for first 3 years is 6% per annum, for the next 4 years, 7 per cent per annum and for the period beyond 7 years, 7.5 percentages per annum. If a man lent out ` 1200 for 11 years, find the total interest earned by him?

1002

912

864

948

Ans .

912 

1. Explanation :

   Whenever it is not mentioned whether we have to assume SI or CI we should assume SI.
   For any amount, interest for the 1st three years @ 6% SI will be equal to 6 × 3 = 18%
   Again, interest for next 4 years will be equal to 7 × 4 = 28%.
   And interest for next 4 years (till 11 years) –7.5 × 4 = 30%
   So, total interest = 18 + 28 + 30 = 76%
   So, total interest earned by him = 76% of the amount = (76*1200 / 100) = 912

Q.

A sum of money doubles itself in 12 years. Find the rate percentage per annum

12.5%

8.33%

10%

7.51%

Ans .

8.33% 

1. Explanation :

   Let principal = x, then interest = x, time = 12 years.
   Using the formula, Rate = (Interest × 100)/Principal × Time
   = (x × 100)/(x × 12) = 8.33%

Q.

A certain sum of money amounts to ` 704 in 2 years and ` 800 in 5 years. Find the principal.

580

600

660

640

Ans .

640 

1. Explanation :

   Let the principal be ` x and rate = r%.
   Then, difference in between the interest of 5 years and of 2 years equals to
   ` 800 – ` 704 = ` 96
   So, interest for 3 years = ` 96
   Hence, interest/year = ` 96/3 = ` 32
   So, interest for 2 years Æ 2 × ` 32 = ` 64
   So, the principal = ` 704 – ` 64 = ` 640

Q.

A sum of money was invested at SI at a certain rate for 3 years. Had it been invested at a 4% higher rate, it would have fetched ` 480 more. Find the principal.

4000

4400

5000

3500

Ans .

4000 

1. Explanation :

   Let the rate be y% and principal be ` x and the time be 3 years.
   Then according to the question = (x(y + 4) × 3)/100 – (xy × 3)/100 = 480
   so xy + 4x – xy = 160 × 100
   so x = (160 × 100)/4 = ` 4000
   

Q.

A certain sum of money trebles itself in 8 years. In how many years it will be five times?

22

16

20

24

Ans .

16 

1. Explanation :

   It trebles itself in 8 years, which makes interest equal to 200% of principal.
   So, 200% is added in 8 years.
   Hence, 400%, which makes the whole amount equal to five times of the principal, which will be added in
   16 years.

Q.

If CI is charged on a certain sum for 2 years at 10% the amount becomes 605. Find the principal?

550

450

480

500

Ans .

500 

1. Explanation :

   Using the formula, amount = Principal (1 + rate/100)time
   605 = p(1 + 10/100)2 = p(11/10)2 
   p = 605(100/121) = ` 500

Q.

If the difference between the CI and SI on a certain sum of money is ` 72 at 12 per cent per annum for 2 years, then find the amount.

6000

5000

5500

6500

Ans .

5000 

1. Explanation :

   Simple interest and compound interest for the first year on any amount is the same.
   Difference in the second year’s interest is due to the fact that compound interest is calculated over the first
   year’s interest also.
   Hence, we can say that ` 72 = Interest on first year’s interest Æ 12% on first year’s interest = ` 72.
   Hence, first year’s interest = ` 600 which should be 12% of the original capital. Hence, original capital =
   ` 5000 (this whole process can be done mentally).

Q.

The population of Jhumri Tilaiya increases by 10% in the first year, it increases by 20% in the second year and due to mass exodus, it decreases by 5% in the third year. What will be its population after 3 years, if today it is 10,000?

11,540

13,860

12,860

12,540

Ans .

12,540 

1. Explanation :

   Population at the end of 1 year will be Æ 10,000 + 10% of 10,000 = 11,000
   At the end of second year it will be 11,000 + 20% of 11,000 = 13,200
   At the end of third year it will be 13,200-5% of 13,200 = 12,540.

Q.

Seth Ankoosh Gawdekar borrows a sum of ` 1200 at the beginning of a year. After 4 months, ` 1800 more is borrowed at a rate of interest double the previous one. At the end of the year, the sum of interest on both the loans is ` 216. What is the first rate of interest per annum?

9

6

8

12

Ans .

6 

1. Explanation :

   Let the rate of interest be = r%
   Then, interest earned from ` 1200 at the end of year = (1200r)/100 = ` 12r
   Again, interest earned from ` 1800 at the end of year = (1800/100) × (8/12) × 2r = ` 24r
   So, total interest earned = 36r, which equals 216
   fi r = 216/36 = 6%

Q.

1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years

1380

1290

1470

1200

Ans .

1380 

1. Explanation :

   The annual interest would be ` 60. After 3 years the total value would be 1200 + 60 × 3 = 1380

Q.

Interest obtained on a sum of ` 5000 for 3 years is ` 1500. Find the rate percen

8

9

10

11

Ans .

10 

1. Explanation :

   The interest earned per year would be 1500/3=500. This represents a 10% rate of interest

Q.

2100 is lent at compound interest of 5% per annum for 2 years. Find the amount after two years

2300

2315.25

2310

2320

Ans .

2315.25 

1. Explanation :

   2100 + 5% of 2100 = 2100 + 105 = 2205 (after 1 year). Next year it would become:
   2205 + 5% of 2205 = 2205 +110.25 = 2315.25

Q.

1694 is repaid after two years at compound interest. Which of the following is the value of the principal and the rate?

1200, 20%

1300, 15%

1400, 10%

1500, 12%

Ans .

1400, 10%

1. Explanation :

   1400 increased by 10% gives 1540 increased by 10% gives  1694.
   

Q.

Find the difference between the simple and the compound interest at 5% per annum for 2 years on a principal of ` 2000

5

10.5

4.5

5.5

Ans .

5 

1. Explanation :

   Simple Interest for 2 years = 100 + 100 = 200.
   Compound interest for 2 years: Year 1 = 5% of 2000 = 100.
   Year 2: 5% of 2100 = 105 Æ Total compound interest = ` 205.
   Difference between the Simple and Compound interest = 205 – 200 = ` 5

Q.

Find the rate of interest if the amount after 2 years of simple interest on a capital of ` 1200 is ` 1440

8

9

10

11

Ans .

10 

1. Explanation :

   Interest in 2 years = ` 240.
   Interest per year = ` 120
   Rate of interest = 10%

Q.

After how many years will a sum of ` 12,500 become ` 17,500 at the rate of 10% per annum?

2

3

4

5

Ans .

4 

1. Explanation :

   12500 @ 10% simple interest would give an interest of ` 1250 per annum. For a total interest of 5000, it would take 4 years.

Q.

What is the difference between the simple interest on a principal of ` 500 being calculated at 5% per annum for 3 years and 4% per annum for 4 years?

5

10

20

40

Ans .

5 

1. Explanation :

   5% for 3 years (SI) = 15% of the amount; At the same time 4% SI for 4 years means 16% of the amount. The difference between the two is 1% of the amount. 1% of 500 = ` 5

Q.

What is the simple interest on a sum of `700 if the rate of interest for the first 3 years is 8% per annum and for the last 2 years is 7.5% per annum?

269.5

283

273

280

Ans .

273 

1. Explanation :

   8% @ 700 = ` 56 per year for 3 years
   7.5% @ 700 = ` 52.5 per year for 2 years
   Total interest = 56 × 3 + 52.5 × 2 = 273

Q.

What is the simple interest for 9 years on a sum of ` 800 if the rate of interest for the first 4 years is 8% per annum and for the last 4 years is 6% per annum?

400

392

352

cant say

Ans .

cant say 

1. Explanation :

   8% of 800 for 4 years + 6% of 800 for 4 years = 64 × 4 + 48 × 4 = 256 + 192 = 448. However, we do not know the rate of interest applicable in the 5
   th year and hence cannot determine the exact
   simple interest for 9 years

Q.

What is the difference between compound interest and simple interest for the sum of ` 20,000 over a 2 year period if the compound interest is calculated at 20% and simple interest is calculated at 23%?

400

460

440

450

Ans .

400 

1. Explanation :

   Simple interest @ 23% = 4600 × 2 = 9200
   Compound interest @ 20%
   20000 increase of 20% 24000 increase of 20% 28800
   so` 8800 compound interest.
   Difference = 9200 – 8800 = ` 400

Q.

Find the compound interest on ` 1000 at the rate of 20% per annum for 18 months when interest is compounded half-yearly

331

1331

320

325

Ans .

331 

1. Explanation :

   1000 increase of 10% gives 1100 increase of 10% gives 1210 increase of 10% gives 1331.
   Compound interest = 1331 – 1000 = ` 331

Q.

Find the principal if the interest compounded at the rate of 10% per annum for two years is ` 420

2000

2200

1000

1100

Ans .

2000 

1. Explanation :

   Solve using options. Thinking about option (a):
   2000 gives 2200 (after 1 year) gives 2420 (after 2 years) which gives us an interest of `420 as required
   in the problem. Hence, this is the correct answer

Q.

Find the principal if compound interest is charged on the principal at the rate of 16 % per annum for two years and the sum becomes ` 196

140

154

150

144

Ans .

144 

1. Explanation :

   P × 7/6 × 7/6 = 196 gives P = (196 × 6 × 6)/7 × 7 = 144

Q.

The SBI lent ` 1331 to the Tata group at a compound interest and got ` 1728 after three years. What is the rate of interest charged if the interest is compounded annually?

11

9.09

12

8.33

Ans .

9.09 

1. Explanation :

   1331 × 1.090909 × 1.090909 × 1.090909 = 1331 × 12/11 × 12/11 × 12/11 = 1728. Hence, the rate of compound interest is 9.09%.

Q.

In what time will ` 3300 become ` 3399 at 6% per annum interest compounded half-yearly?

6 months

1 year

1.5 years

3 months

Ans .

6 

1. Explanation :

   Since compounding is half yearly, it is clear that the rate of interest charged for 6 months would be 3%. Thus we get 3300 gives 3% increase and we get 3399

Q.

Ranjan purchased a Maruti van for ` 1,96,000 and the rate of depreciation is 14 2/7% per annum. Find the value of the van after two years

140000

144000

150000

160000

Ans .

144000  

1. Explanation :

   The value of the van would be 196000 × 6/7 × 6/7 = 144000

Q.

At what percentage per annum, will ` 10,000 amount to 17,280 in three years? (Compound Interest being reckoned)

20

14

24

11

Ans .

20 

1. Explanation :

   Solve through options:
   10000 with 20% increase gives 12000 with 20% increase gives 14400 with 20% increase gives 17280.

Q.

Vinay deposited ` 8000 in ICICI Bank, which pays him 12% interest per annum compounded quarterly. What is the amount that he receives after 15 months?

9274.2

9228.8

9314.3

9338.8

Ans .

9274.2 

1. Explanation :

   12% per annum compounded quarterly means that the amount would grow by 3% every 3 months. Thus, 8000 gives 8000 + 3% of 8000 = 8240 after 3 months gives 8240 + 3% of 8240 = 8487.2 after 6
   months and so on till five3 month time periods get over. It can be seen that the value would turn out to be 9274.2.
   

Q.

What is the rate of simple interest for the first 4 years if the sum of ` 360 becomes ` 540 in 9 years and the rate of interest for the last 5 years is 6%?

4

5

3

6

Ans .

5 

1. Explanation :

   For the last 5 years, the interest earned would be: 30% of 360 = 108. Thus, interest earned in the first 4 years would be ` 72 and  ` 18 every year on an amount of ` 360- which means that the rate of
   interest is 5%
   

Q.

Harsh makes a fixed deposit of ` 20,000 with the Bank of India for a period of 3 years. If the rate of interest be 13% SI per annum charged half-yearly, what amount will he get after 42 months?

27800

28100

29100

28500

Ans .

29100 

1. Explanation :

   He will get 20000 + 45.5% of 20000 = 29100.
   [Note: In this case we can take 13% simple interest compounded half yearly to mean 6.5% interest
   getting added every 6 months. Thus, in 42 months it would amount to 6.5 × 7 = 45.5%

Q.

Ranjeet makes a deposit of ` 50,000 in the Punjab National Bank for a period of years. If the rate of interest is 12% per annum compounded half-yearly, find the maturity value of the money deposited by him.

66,911.27

66,123.34

67,925.95

65,550.8

Ans .

66911.27 

1. Explanation :

   50000 gives with a 6% interest per annum 53000 gives with a 6% interest per annum 56180 gives with a 6% interest per annum 59550.8 gives with a 6% interest per annum 63123.84 gives with a 6% interest per annum
   66911.27

Q.

Vinod makes a deposit of ` 100,000 in Syndicate Bank for a period of 2 years. If the rate of interest be 12% per annum compounded half-yearly, what amount will he get after 2 years?

122,247.89

125,436.79

126,247.69

122436.89

Ans .

126247.69 

1. Explanation :

   100000 + 6% of 100000 (after the first 6 months) = 106000.
   After 1 year: 106000 + 6% of 106000 = 112360
   After 1 ½ years: 112360 + 6% of 112360 = 119101.6
   After 2 years: 119101.6 + 6% of 119101.6 = 126247.69

Q.

What will be the simple interest on ` 700 at 9% per annum for the period from February 5, 1994 to April 18, 1994?

12.60

11.30

15

13

Ans .

12.6 

1. Explanation :

   (73/365) × 0.09 × 700 = ` 12.6.
   (Since the time period is 73 days)

Q.

Ajay borrows ` 1500 from two moneylenders. He pays interest at the rate of 12% per annum for one loan and at the rate of 14% per annum for the other. The total interest he pays for the entire year is ` 186. How much does he borrow at the rate of 12%?

1200

1300

1400

300

Ans .

1200 

1. Explanation :

   The average rate of interest he pays is 186 × 100/1500 = 12.4%.
   The average rate of interest being 12.4%, it means that the ratio in which the two amounts would
   be distributed would be 4:1 (using alligation). Thus, the borrowing at 12% would be ` 1200

Q.

A sum of money placed at compound interest doubles itself in 3 years. In how many years will it amount to 8 times itself?

9

8

27

7

Ans .

9 

1. Explanation :

   If it doubles in 3 years, it would become 4 times in 6 year and 8 times in 9 years

Q.

A difference between the interest received from two different banks on ` 400 for 2 years is ` 4. What is the difference between their rates?

0.5

0.2

0.23

0.52

Ans .

0.5 

1. Explanation :

   The difference in Simple interest represents 1% of the amount invested. Since this difference has occurred in 2 years, annually the difference would be 0.5%.

Q.

A sum of money doubles itself in 5 years. In how many years will it become four fold (if interest is compounded)?

15

10

20

12

Ans .

10 

1. Explanation :

   It would take another 5 years to double again. Thus, a total of 10 years to become four fold

Q.

A sum of money becomes 4 times at simple interest in 10 years. What is the rate of interest?

10

20

30

40

Ans .

30 

1. Explanation :

   The sum becomes 4 times Æ the interest earned is 300% of the original amount. In 10 years the interest is 300% means that the yearly interest must be 30%

Q.

What annual payment will discharge a debt of ` 808 due in 2 years at 2% per annum?

200

300

400

350

Ans .

400 

1. Explanation :

   A × (1.02) + A = 808 × (1.02)
   2 Æ A = ` 400

Q.

In what time will ` 8000 amount to 40,000 at 4% per annum? (simple interest being reckoned)

100

50

110

160

Ans .

100 

1. Explanation :

   The value would increase by 4% per year. To go to 5 times it’s original value, it would require an increment of 400%. At 4% SI it would take 100 years

Q.

Raju lent ` 400 to Ajay for 2 years, and ` 100 to Manoj for 4 years and received together from both ` 60 as interest. Find the rate of interest, simple interest being calculated

5

6

8

9

Ans .

5 

1. Explanation :

   Total effective amount lent for 1 year
   = ` 400 × 2 + ` 100 × 4 = ` 1200
   Interest being ` 60, Rate of interest 5%

Q.

If the difference between the simple interest and compound interest on some principal amount at 20% per annum for 3 years is ` 48, then the principle amount must be

550

500

375

400

Ans .

375 

1. Explanation :

   Solve using options. If we try 500 (option b) for convenience, we can see that the difference between the two is ` 64 (as the SI would amount to 300 and CI would amount to 100 + 120 + 144
   = 364). Since, we need a difference of only ` 48 we can realize that the value should be 3/4
   th of 500. Hence, 375 is correct

Q.

Shashikant derives an annual income of ` 688.25 from ` 10,000 invested partly at 8% p.a. and partly at 5% p.a. simple interest. How much of his money is invested at 5% ?

5000

4225

4800

3725

Ans .

3725 

1. Explanation :

   The average Rate of interest is 6.8825%. The ratio of investments would be 1.1175: 1.8825 (@5% is to 8%). The required answer = 10000 × 1.1175/3 = 3725

Q.

In what time will ` 500 give ` 50 as interest at the rate of 5% per annum simple interest?

2

5

3

4

Ans .

2 

1. Explanation :

   Interest per year = ` 25. Thus, an interest of ` 50 would be earned in 2 years.

Q.

In what time will the simple interest on ` 1750 at 9% per annum be the same as that on ` 2500 at 10.5% per annum in 4 years?

6 years and 8 months

7 years and 3 months

6 years

7 years and 6 months

Ans .

6 years and 8 months 

1. Explanation :

   42% on 2500 = ` 1050. The required answer would be: 1050/157.5 = 6 years and 8 months.

Q.

Two equal sums were borrowed at 8% simple interest per annum for 2 years and 3 years respectively. The difference in the interest was ` 56. The sum borrowed were

690

700

740

780

Ans .

700 

1. Explanation :

   The difference would amount to 8% of the value borrowed. Thus 56 = 0.08 × sum borrowed in each case becomes Sum borrowed = ` 700.

Q.

A sum of money is borrowed and paid back in two equal annual instalments of ` 882, allowing 5% compound interest. The sum borrowed was

1640

1680

1620

1700

Ans .

1640 

1. Explanation :

   882 × (1.05) + 882 = P × (1.05)2
   Solve for P to get P = 1640

Q.

The difference between simple and compound interest on a sum of money at 5% per annum is ` 25. What is the sum?

5000

10000

4000

data insufficient

Ans .

data insufficient 

1. Explanation :

   The data is insufficient as we do not know the time period involved.
   

Q.

A sum was invested at simple interest at a certain interest for 2 years. It would have fetched ` 60 more had it been invested at 2% higher rate. What was the sum?

1500

1300

2500

1000

Ans .

1500 

1. Explanation :

   Based on the information we have, we can say that there would have been ` 30 extra interest per year. For 2% of the principal to be equal to ` 30, the principal amount should be ` 1500

Problems

Q. Find the simple interest on Rs. 3000 at rate of interest 6 1/4% for 73 days

A. 73 days = 73/365 = 1/5 yrs.

SI = (3000 * 25/4 * 1/5) / 100

Q. An amount loaned at interest rate 13.5% per annum becomes Rs. 2502.50 after 4 years. Find the sum.

A. P + SI = P + P * 13.5 * 4 / 100 (Adding P on both sides)

2502.5 = P ( 1 + 54/100)

2502.5 = P (1.54)

P = 2502.5 / 1.54 = 1625

Q. A borrowed money at interest rate 6% for first two years, 9% for next three years and 14% for period beyond 5 years. If he pays a total interest of Rs. 11400 after 9 yrs how much did he borrow?

A. 11400 = (P *6*2/100) + (P*9*3/100) + (P*14*4/100)

11400 = (12+27+56)P / 100

11400 * 100 / 95 = P

P = 12000

Q. A certain sum of money amounts to Rs 1008 in 2 years and Rs. 1164 in 3.5 yrs.Find sum and RI

A. SI for 1.5 yrs = 1164 - 1008 = 156

SI for 1 yrs = 156 * 2 / 3 = 104 and two years = 208.

Principal = 1008 - 208 = 800

Use simple interest formula to get RI.

Q. A sum of 1500 is lent in 2 parts where one is at 8% and second is at 6%. If the total annual income is Rs. 106, find money lent at each rate.

A. (x*1*8/100) + ((1500-x) * 1 * 6 / 100 ) = 106

8x/100 + (9000 - 6x)/100 = 106

8x +9000 - 6x = 10600

2x = 1600

x=800

Compound Interest

When P = principal, n = years and R = rate of interest compounded annually

The Amount = P (1+R/100)^n

When P = principal, R = rate of interest compounded annually but is different for first year R1, second year R2 and third year R3 then
Amount = P ( 1 + R1 / 100) * ( 1 + R2 / 100) * ( 1 + R3 / 100)

Present worth of Rs. x due n years hence is
Present worth = x / (1 + R/100)^n

Solved Problems

Q. Find CI on Rs.7500, compounded annually at RI of 4% for 2 years.

A. Amount = 7500 * (1 + 4/100)^2

Then amount - 7500 gives CI.

Q. CI is compounded half yearly, principal = Rs. 10000 in rate 4% for 2 years.

A.  Amount = 10000( 1+ 2/100)^4

Amount = 10824.32

CI = Amount - principal = 10824.32 - 10000 = 824.32

Q. Difference between SI and CI accrued on an amount of Rs. 18000 in 2 years is Rs.405. What is the RI.

A. P( 1+ (R/100) )^n - P*R*T/100 = 405

{18000 ( 1 + (R/100))^2 - 18000}  - (18000 * R * 2 / 100) = 405

Solving this you can get R.

Q. Divide 1301 between A and B such that the amount of A after 7 years is equal to amount in B after 9 years. Interest is compounded at 4%.

A. Let the amount be 'x' and 1301 - x.

x(1+4/100)^7 = (1301-x)(1+4/100)^9

Solving this we can get 'x'.

Q. A sum of money amounts to Rs.6690 after 3 years and Rs. 10035 after 6 years on CI. Find the sum.

A. P(1+R/100)^3 = 6690 ; P(1+R/100)^6 = 10035

Dividing first eqn by second eqn we get (1+R/100)^3 = 10035/6690 = 3/2

Substituting this value in first equation we get P = 6690 * 2 / 3 = 4460.

Q. A sum doubles itself in 9 years how many will it take to become 8 times.

A. P(1+R/100)^9 = 2P

(1+R/100)^9 = 2

Now finding P(1+R/100)^n = 8P

we need to get (1 + R/100)^n = 8 but 8 = 2^3

(1+R/100)^n = (1 + R/100)^ 9 ^3

we know that A^b^c = A^b*c

so (1+R/100)^n = (1 + R/100)^ 9*3 = (1 + R/100)^27

n = 27

CAT Problems

Q.A sum of money compounded annually becomes Rs.625 in two years and Rs.675 in three years. The rate of interest per annum is

1. 7
2. 8
3. 6
4. 5

Ans.b

Quiz

Score more than 80% marks and move ahead else stay back and read again!