RD Sharma solution class 7 chapter 13 Simple Interest Exercise 13.1

Exercise 13.1

Page-13.7

Question 1:

Find the simple interest, when:
(i) Principal = Rs 2000, Rate of Interest = 5% per annum and Time = 5 years.
(ii) Principal = Rs 500, Rate of Interest = 12.5% per annum and Time = 4 years.
(iii) Principal = Rs 4500, Rate of Interest = 4% per annum and Time =  months.
(iv) Principal = Rs 12000, Rate of Interest = 18% per annum and Time = 4 months.
(v) Principal = Rs 1000, Rate of Interest = 10% per annum and Time = 73 days.

Answer 1:

(i) Principal (P) = Rs 2000
Rate of interest (R) = 5% p.a.
Time (T) = 5 years
Simple interest =  $\frac{P\times R\times T}{100}=\frac{2000\times 5\times 5}{100}=\mathrm{Rs} 500$

(ii)  Principal (P) = Rs 500
Rate of interest (R) = 12.5% p.a.
Time (T) = 4 years
Simple interest = $\frac{P\times R\times T}{100}=\frac{500\times 12.5\times 4}{100}=\mathrm{Rs} 250$

(iii) Principal (P) = Rs 4500
Rate of interest (R) = 4% p.a.
Time (T) = 6 months

T =$\frac{6}{12}=\frac{1}{2}$ year (1 year = 12 months)
Simple interest = $\frac{P\times R\times T}{100}=\frac{4500\times 4\times {\displaystyle \frac{1}{2}}}{100}=\frac{4500\times 4\times 1}{100\times 2}=\mathrm{Rs} 90$

(iv) Principal (P) = Rs 12000
Rate of interest (R) = 18% p.a.
$Time\; (T)\; =\; 4 months =\frac{4}{12}=\frac{1}{3}\text{y}\mathrm{ear}$       (1 year = 12 months)

Simple interest = $\frac{P\times R\times T}{100}=\frac{12000\times 18\times 1}{100\times 3}=\mathrm{Rs} 720$

(v) Principal (P) = Rs 1000
Rate of interest (R) = 10% p.a.
$\mathrm{Time\; (}T)\; =\; 73 days = \frac{73}{365} \mathrm{year}$   (1 year = 365 days)

Simple interest = $\frac{P\times R\times T}{100}=\frac{1000\times 10\times 73}{100\times 365}=\mathrm{Rs} 20$

Page-13.8

Question 2:

Find the interest on Rs 500 for a period of 4 years at the rate of 8% per annum. Also, find the amount to be paid at the end of the period.

Answer 2:

Principal amount (P) = Rs 500
Time period (T) = 4 years
Rate of interest (R)  = 8% p.a.

 Interest = $\frac{P\times R\times T}{100}=\frac{500\times 4\times 8}{100}=\mathrm{Rs} 160$

Total amount paid = Principal amount + Interest = Rs 500 + 160
                                                                         = Rs 660

Question 3:

A sum of Rs 400 is lent at the rate of 5% per annum. Find the interest at the end of 2 years.

Answer 3:

Principal amount (P) = Rs 400
Time period (T) = 2 years
Rate of interest (R)  = 5% p.a.

Interest paid after 2 years$=\frac{P\times R\times T}{100}=\frac{400\times 5\times 2}{100}=\mathrm{Rs} 40$

Question 4:

A sum of Rs 400 is lent for 3 years at the rate of 6% per annum. Find the interest.

Answer 4:

Principal amount (P) = Rs 400
Time period (T) = 3 years
Rate of interest (R)  = 6% p.a.
Interest after 3 years = $\frac{P\times R\times T}{100}=\frac{400\times 6\times 3}{100}$ = Rs 72

Question 5:

A person deposits Rs 25000 in a firm who pays an interest at the rate of 20% per annum. Calculate the income he gets from it annually.

Answer 5:

Principal amount (P) = Rs 25000
Time period (T) = 1 year
Rate of interest (R)  = 20% p.a.
Annual interest = $\frac{P\times R\times T}{100}=\frac{25000\times 20\times 1}{100}$ = Rs 5000

Question 6:

A man borrowed Rs 8000 from a bank at 8% per annum. Find the amount he has to pay after $4\frac{1}{2}$ years.

Answer 6:

Principal amount (P) = Rs 8000
Time period (T) = $4\frac{1}{2}=\frac{9}{2} \mathrm{years}$
Rate of interest (R)  = 8% p.a.
Interest = $\frac{P\times R\times T}{100}=\frac{8000\times 8\times 9}{100\times 2}$ = Rs 2880

Total amount paid after $4\frac{1}{2}$ years  = Principal amount + Interest = Rs 8000 + Rs 2880
                                                                                                 = Rs 10880

Question 7:

Rakesh lent out Rs 8000 for 5 years at 15% per annum and borrowed Rs 6000 for 3 years at 12% per annum. How much did he gain or lose?

Answer 7:

Principal amount lent out by Rakesh (P) = Rs 8000
Time period (T) = 5 years
Rate of interest (R)  = 15% p.a.
Interest = $\frac{P\times R\times T}{100}=\frac{8000\times 15\times 5}{100}$ = Rs 6000

Principal amount borrowed by Rakesh (P) = Rs 6000
Time period (T) = 3 years
Rate of interest (R) = 12% p.a.
 Interest = $\frac{P\times R\times T}{100}=\frac{6000\times 12\times 3}{100}$ = Rs 2160

Amount gained by Rakesh = Rs 6000 − Rs 2160 = Rs 3840

Question 8:

Anita deposits Rs 1000 in a savings bank account. The bank pays interest at the rate of 5% per annum. What amount can Anita get after one year?

Answer 8:

Principal amount (P) = Rs 1000
Time period (T) = 1 year
Rate of interest (R) = 5% p.a.

 Interest = $\frac{P\times R\times T}{100}=\frac{1000\times 5\times 1}{100}$ = Rs 50

Total amount paid after 1 year = Principal amount + Interest = Rs 1000 + Rs 50
                                                                                           = Rs 1050

Question 9:

Nalini borrowed Rs 550 from her friend at 8% per annum. She returned the amount after 6 months. How much did she pay?

Answer 9:

Principal amount (P) = Rs 550
Time period (T)  = 6 months = $\frac{6}{12}=\frac{1}{2}$ year        (1 year = 12 months)
Rate of interest (R)  = 8% p.a.

 Interest = $\frac{P\times R\times T}{100}=\frac{550\times 8\times 1}{100\times 2}=\mathrm{Rs} 22$

Total amount paid after 6 months = Principal amount + Interest = Rs 550 + Rs 22
                                                                                               = Rs 572

Question 10:

Rohit borowed Rs 600000 from a bank at 9% per annum for 2 years. He lent this sum of money to Rohan at 10% per annum for 2 years. How much did Rohit earn from this transaction?

Answer 10:

Principal amount lent out by Rohit (P) = Rs. 60000
Time period (T)        = 2 years
Rate of interest (R)  = 10% p.a.

 Interest = $\frac{P\times R\times T}{100}=\; Rs.\frac{60000\times 10\times 2}{100}=\; Rs.\; 12000$

Principal amount borrowed by Rohit from the bank (P) = Rs. 60000
Time period (T)                                         = 2 years
Rate of interest (R)                                   = 9% p.a.
 Interest = $\frac{P\times R\times T}{100}=\; Rs.\frac{60000\times 9\times 2}{100}=\; Rs.\; 10800$

Amount gained by Rohit = Rs. 12000 - 10800 = Rs. 1200

Question 11:

Romesh borrowed Rs 2000 at 2% per annum and Rs 1000 at 5% per annum. He cleared his debt after 2 years by giving Rs 2800 and a watch. What is the cost of the watch?

Answer 11:

Principal amount borrowed by Romesh (P) = Rs. 2000
Time period (T)        = 2 years
Rate of interest (R)  = 2% p.a.

 Interest = $\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{T}}{100}= \mathrm{Rs}.\frac{2000\times 2\times 2}{100}= \mathrm{Rs}.80$

Principal amount borrowed by Romesh (P) = Rs. 1000
Time period (T)        = 2 years
Rate of interest (R)  = 5% p.a.

 Interest = $\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{T}}{100}=\mathrm{Rs}.\frac{1000\times 5\times 2}{100}= \mathrm{Rs}.100$

Total amount that he will have to return  = Rs. 2000 + 1000 + 80 + 100 = Rs. 3180

Amount repaid = Rs. 2800
Value of the watch = Rs. 3180 - 2800 = Rs. 380

Question 12:

Mr Garg lent Rs 15000 to his friend. He charged 15% per annum on Rs 12500 and 18% on the rest. How much interest does he earn in 3 years?

Answer 12:

Principal amount (P) = Rs 12500
Time period (T) = 3 years
Rate of interest (R)  = 15% p.a.

Interest = $\frac{P\times R\times T}{100}=\frac{12500\times 15\times 3}{100}$ = Rs 5625

Rest of the amount lent =  Rs 15000 − Rs 12500 = Rs 2500
Rate of interest = 18 % p.a.
Time period = 3 years

 Interest = $\frac{P\times R\times T}{100}=\frac{2500\times 18\times 3}{100}$ = Rs 1350

Total interest earned = Rs 5625 + Rs 1350 = Rs 6975

Question 13:

Shikha deposited Rs 2000 in a bank which pays 6% simple interest. She withdrew Rs 700 at the end of first year. What will be her balance after 3 years?

Answer 13:

Principal amount deposited  (P) = Rs 2000
Time period (T) = 1 year
Rate of interest (R)  = 6% p.a.
Interest after 1 year = $\frac{P\times R\times T}{100}=\frac{2000\times 6\times 1}{100}=\mathrm{Rs} 120$
So amount after 1 year = Principal amount + Interest = 2000 + 120 = Rs 2120
After 1 year, amount withdrawn = Rs 700
Principal amount left (P₁) = Rs 2120 − Rs 700 = Rs 1420
Time period (T) = 2 years
Rate of interest (R)  = 6% p.a.
 Interest after 2 years = $\frac{P_1\times R\times T}{100}=\frac{1420\times 6\times 2}{100}=\mathrm{Rs} 170.40$

Total amount after 3 years = Rs 1420  + Rs 170.40 = Rs 1590.40

Question 14:

Reema took a loan of Rs 8000 from a money lender, who charged interest at the rate of 18% per annum. After 2 years, Reema paid him Rs 10400 and wrist watch to clear the debt. What is the price of the watch?

Answer 14:

Principal amount (P) = Rs 8,000
Rate of interest (R) = 18%
Time period (T) = 2 years
Interest after 2 years = $\frac{P\times R\times T}{100}=\frac{8000\times 18\times 2}{100}$ = Rs 2,880
Total amount payable by Reema after 2 years = Rs 8,000 + Rs 2,880 = Rs 10,880
Amount paid = Rs 10,400
Value of the watch = Rs 10,880 − Rs 10,400 = Rs 480

Question 15:

Mr Sharma deposited Rs 20000 as a fixed deposit in a bank at 10% per annual. If 30% is deducted as income tax on the interest earned, find his annual income.

Answer 15:

Amount deposit (P) = Rs 20,000
Rate of interest (R) = 10% p.a.
Time period (T) = 1 year

Interest after 1 year = $\frac{P\times R\times T}{100}=\frac{20000\times 10\times 1}{100}$ = Rs 2,000

Amount deducted as income tax = $30\% \mathrm{of} \mathrm{Rs} 2,000 =\frac{30\times 2000}{100}=\mathrm{Rs} 600$

Annual interest after tax deduction = Rs 2,000 − Rs 600 = Rs 1,400