SELINA Solution Class 9 Compound interest (without using formula) Chapter 2 Exercise 2A

Question 1

Rs.16,000 is invested at 5% compound interest compounded per annum. Use the table, given below, to find the amount in 4 years.

Year ↓	Initial amount  (Rs.)	Interest (Rs.)	Final amount (Rs.)
1st	16,000	800	16,800
2nd	...........	...........	...........
3rd	...........	...........	...........
4th	...........	...........	...........
5th	...........	...........	...........

Sol:

Year ↓	Initial amount  (Rs.)	Interest (Rs.)	Final amount (Rs.)
1st	16,000	800	16,800
2nd	16,800	840	17,640
3rd	17,640	882	18,522
4th	18,522	926.10	19,448.10
5th	19,448.10	972.405	20,420.505

Thus, the amount in 4 years is Rs. 19448.10.

Question 2.1

Calculate the amount and the compound interest on :
Rs. 6,000 in 3 years at 5% per year.

Sol:

For 1^st year,
P = Rs. 6,000; R = 5%, and T = 1 year
∴ Interest = Rs. ${\displaystyle \frac{6,000\times 5\times 1}{100}}$ = Rs. 300.
And, amount = Rs. ( 6,000 + 300 ) = Rs. 6,300
For 2nd year,
P = Rs. 6,300; R = 5%, and T = 1 year
∴ Interest = Rs. ${\displaystyle \frac{6,300\times 5\times 1}{100}}$ = Rs. 315
And, amount = Rs. ( 6,300 + 315 ) = Rs. 6,615
For 3rd year,
P = Rs. 6,615; R = 5% and T = 1 year
∴ Interest = Rs. ${\displaystyle \frac{6,615\times 5\times 1}{100}}$ = Rs. 330.75
And, Amount = Rs. ( 6,615 + 330.75 ) = Rs. 6,945.75
∴ C.I. accrued = Final amount - Intitial Principal
                       = Rs. ( 6,945.75 - 6,000 )
                       = Rs. 945.75

Question 2.2

Calculate the amount and the compound interest on :
Rs. 8,000 in ${\displaystyle 2\frac{1}{2}}$ years at 15% per year.

Sol:

For 1^st year,
P = Rs. 8,000; R = 15%, and T = 1 year

∴ Interest = Rs. ${\displaystyle \frac{8,000\times 15\times 1}{100}}$ = Rs. 1200.

And, amount = Rs. ( 8,000 + 1200 ) = Rs. 9,200
For 2^nd year,
P = Rs. 9,200; R = 15%, and T = 1 year

∴ Interest = Rs. ${\displaystyle \frac{9,200\times 15\times 1}{100}}$ = Rs. 1,380.

And, amount = Rs. ( 9,200 + 1,380 ) = Rs. 10,580
For the last  ${\displaystyle \frac{1}{2}}$ year,
P = Rs. 10,580 ; R = 15% and T = ${\displaystyle \frac{1}{2}}$ year

∴ Interest = Rs. ${\displaystyle \frac{10,580\times 15\times 1}{100\times 2}}$ = Rs. 793.50

And, Amount = Rs. ( 10,580 + 793.50 ) = Rs. 11373.50

∴ C.I. accrued = Final amount - Intitial Principal
                       = Rs. ( 11,373.50 - 8,000 )
                       = Rs. 3373.50

Question 3.1

Calculate the amount and the compound interest on :
₹ 4,600 in 2 years when the rates of interest of successive years are 10%and 12% respectively.

Sol:

For 1^st year
P = Rs. 4600
R = 10%
T = 1 year.

I = ${\displaystyle \frac{4600\times 10\times 1}{100}}$ = Rs. 460

A = 4600 + 460 = Rs. 5060

For 2^nd year
P = Rs. 5060
R = 12%
T = 1 year.

I = ${\displaystyle \frac{5060\times 12\times 1}{100}=\frac{60720}{100}=607.20}$

A= 5060 + 607.20 = Rs. 5667.20

Compound interest = 5667.20 - 4600 = Rs. 1067.20

Amount after 2 years = Rs. 5667.20

 

Question 3.2

Calculate the amount and the compound interest on :
Rs. 16,000 in 3 years, when the rates of the interest for successive years are 10%, 14% and 15% respectively.

Sol:

For 1^st year
P = Rs. 16000
R = 10%
T = 1 year

I = ${\displaystyle \frac{16000\times 10\times 1}{100}}$ = Rs. 1600

A = 16000 + 1600 = 17600

For 2^nd year,
P = Rs. 17600
R = 14%
T = 1 year

I = ${\displaystyle \frac{17600\times 14\times 1}{100}=\frac{246400}{100}}$ = Rs. 2464.

A = 1760 + 24654 = Rs. 20064

For 3^rd year,
P = Rs. 20064
R = 15%
T = 1 year

I = ${\displaystyle \frac{20064\times 15\times 1}{100}}$ = 3009.60

Amount after 3 years = 20064 + 3009.60 = Rs. 23073.60

Compound interest = 23073.60 - 16000 = Rs. 7073.60

Question 4

Find the compound interest, correct to the nearest rupee, on Rs. 2,400 for ${\displaystyle 2\frac{1}{2}}$ years at 5 per cent per annum.

Sol:

For 1^st years
P = Rs. 2400
R = 5%
T = 1 year

I = ${\displaystyle \frac{2400\times 5\times 1}{100}}$ = 120

A = 2400 + 120 = Rs. 2520

For 2^nd year
P = Rs. 2520
R = 5%
T = 1 year

I = ${\displaystyle \frac{2520\times 5\times 1}{100}}$ = Rs. 126.

A = 2520 + 126 = Rs. 2646

For final ${\displaystyle \frac{1}{2}}$ year,
P = Rs. 2646
R = 5%
T = ${\displaystyle \frac{1}{2}}$ year

I = ${\displaystyle \frac{2646\times 5\times 1}{100\times 2}}$ = Rs. 66.15

Amount after ${\displaystyle 2\frac{1}{2}}$ years = 2646 + 66.15 = Rs. 2712.15

Compound interest = 2712.15 - 2400 = Rs. 312.15

 

Question 5

Calculate the compound interest for the second year on Rs. 8,000/- invested for 3 years at 10% per annum.

Sol:

For 1^st year
P = Rs. 8000
R = 10%
T = 1 year

I = ${\displaystyle \frac{8000\times 10\times 1}{100}}$ = 800

A = 8000 + 800 = Rs. 8800
For 2^nd year
P = Rs. 8800
R = 10%
T = 1 year

I = ${\displaystyle \frac{8800\times 10\times 1}{100}}$
Compound interest for 2^nd years = Rs. 880

Quesiton 6

A borrowed Rs. 2,500 from B at 12% per annum compound interest. After 2 years, A gave Rs. 2,936 and a watch to B to clear the account. Find the cost of the watch.

Sol:

For 1^st year,
P = Rs. 2500
R = 12%
T = 1 year

I = ${\displaystyle \frac{2500\times 12\times 1}{100}}$ = Rs. 300.

Amount = 2500 + 300 = Rs. 2800

For 2^nd year,
P = Rs. 2800
R = 12%
T = 1 year

I = ${\displaystyle \frac{2800\times 12\times 1}{100}}$ = Rs. 336

Amount = 2800 + 336 = Rs. 3136

Amount repaid by A to B = Rs. 2936

The amount of watch =Rs. 3136 - Rs. 2936 = Rs. 200

Question 7

---

Sol:

Interest for the first year = ${\displaystyle \frac{\text{P}\times \text{R}\times \text{T}}{100}}$                         

                                        = ${\displaystyle \frac{50,000\times 6\times 1}{100}}$
                                        = Rs. 3,000
Amount for the first year = Rs. 50,000 + Rs. 3,000 = Rs. 53,000

Interest for the second year = ${\displaystyle \frac{\text{P}\times \text{R}\times \text{T}}{100}}$

                                             = ${\displaystyle \frac{53,000\times 8\times 1}{100}}$
                                             = Rs. 4,240

Amount for the second year = Rs. 53,000 + Rs. 4,240 = Rs. 57,240

Interest for the third year = ${\displaystyle \frac{\text{P}\times \text{R}\times \text{T}}{100}}$   

                                          = ${\displaystyle \frac{57,240\times 10\times 1}{100}}$

                                          = Rs. 5,724

Amount for the third year = Rs. 57,240 + Rs. 5,724 = Rs. 62,964
Hence, the amount will be Rs. 62,964.

Question 8

Meenal lends Rs. 75,000 at C.I. for 3 years. If the rate of interest for the first two years is 15% per year and for the third year it is 16%, calculate the sum Meenal will get at the end of the third year.

Sol:

Interest for the first year = ${\displaystyle \frac{\text{P}\times \text{R}\times \text{T}}{100}}$                         

                                       = ${\displaystyle \frac{75,000\times 15\times 1}{100}}$
                                        = Rs. 11,250
Amount for the first year = Rs. 75,000 + Rs. 11,250 = Rs. 86,250

Interest for the second year = ${\displaystyle \frac{\text{P}\times \text{R}\times \text{T}}{100}}$

                                             = ${\displaystyle \frac{86,250\times 15\times 1}{100}}$
                                             = Rs. 12,937.5

Amount for the second year = Rs. 86,250 + Rs. 12,937.5 = Rs. 99,187.5

Interest for the third year = ${\displaystyle \frac{\text{P}\times \text{R}\times \text{T}}{100}}$   

                                          = ${\displaystyle \frac{99,187.5\times 16\times 1}{100}}$

                                          = Rs. 15,870

Amount for the third year = Rs. 99,187.5 + Rs. 15,870 = Rs. 1,15,057.5
Hence, the sum Meenal will get at the end of the third year is Rs. 1,15,057.5

Question 9

Govind borrows Rs18,000 at 10% simple interest. He immediately invests the money borrowed at 10% compound interest compounded half-yearly. How much money does Govind gain in one year ?

Sol:

To calculate S.I.
P = Rs. 18,000; R = 10% and T = 1 year
S.I. = Rs. ${\displaystyle \frac{18,000\times 10\times 1}{100}}$ = Rs. 1,800.

To calculate C.I.
For 1^st half- year :
P= Rs. 18,000; R = 10 % and T= ${\displaystyle \frac{1}{2}}$ year

Interest = Rs. ${\displaystyle \frac{18,000\times 10\times 1}{100\times 2}}$ = Rs. 900

Amount = Rs. 18,000 + Rs. 900 = Rs. 18,900

For 2^nd year : 
P= Rs. 18,900; R = 10% and T = ${\displaystyle \frac{1}{2}}$ year

Interest= Rs. ${\displaystyle \frac{18,900\times 10\times 1}{100\times 2}}$ = Rs. 945.

Amount= Rs. 18,900 + Rs. 945 = Rs. 19,845

Compound interest = Rs. 19,845 - Rs. 18,000 = Rs. 1,845

His gain = Rs. 1,845 - Rs. 1,800= Rs. 45

Quesiton 10

Find the compound interest on Rs. 4,000 accrued in three years, when the rate of interest is 8% for the first year and 10% per year for the second and the third years.

Sol:

Interest for the first year = ${\displaystyle \frac{\text{P}\times \text{R}\times \text{T}}{100}}$                         

                                        = ${\displaystyle \frac{4,000\times 8\times 1}{100}}$
                                        = Rs. 3,20
Amount for the first year = Rs. 4,000 + Rs. 3,20 = Rs. 4,320

Interest for the second year = ${\displaystyle \frac{\text{P}\times \text{R}\times \text{T}}{100}}$

                                             = ${\displaystyle \frac{4,320\times 10\times 1}{100}}$
                                             = Rs. 432

Amount for the second year = Rs. 4,320 + Rs. 432 = Rs. 4,752

Interest for the third year = ${\displaystyle \frac{\text{P}\times \text{R}\times \text{T}}{100}}$   

                                          = ${\displaystyle \frac{4,752\times 10\times 1}{100}}$

                                          = Rs. 475.20

Amount for the third year = Rs. 4,752 + Rs. 475.20 = Rs. 5,227.20

So, the compound interest = Rs. 5,227.20 - Rs. 4,000 = Rs. 1,227.20

Hence, the amount will get at the end of the third year is Rs. 1,227.50.