**Exercise 13.1**

*Q 1. Find the simple interestÂ , when :*

**SOLUTION :**

**(i) . Principal = Rs . 2000 , Rate of interest = 5% per annum , and Time = 5 years **

(i) . Principal (P) = Rs 2000

Rate of interest (R) = 5% p.a.

Time (T) = 5 years

Simple interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{2000\times 5\times 5}{100} \right )\)

**(ii) . Principal = Rs . 500 , Rate of interest = 12.5% per annum , and Time = 4 years **

(ii) . Principal (P) = Rs 500

Rate of interest (R) = 12.5% p.a.

Time (T) = 4 years

Simple interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

=\(\left ( \frac{500\times 12.5\times 4}{100} \right )\)

**(iii) . Principal = Rs . 4500 , Rate of interest = 4% per annum , and Time = 6 months Â **

(iii) . Principal (P) = Rs 4500

Rate of interest (R) = 4% p.a.

Time (T) = 6 months

T = \(\frac{6}{12}\)

Simple interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \( (\frac{4500\times 4\times\frac{1}{2}}{100})\)

=Rs 90

**(iv) . Principal =Rs . 12000Â , Rate of interest = 18% per annum , and Time = 4 months**

(iv) . Principal (P) = Rs 12000

Rate of interest (R) = 18% p.a.

Time (T) = 4 months =\(\frac{4}{12}\)

(1 year = 12 months)

Simple interest =Â \(\left ( \frac{P\times R\times T}{100} \right )\)

= \((\frac{12000\times 18\times\frac{4}{12}}{100})\)

**(v) . Principal = Rs . 1000 , Rate of interest = 10% per annum , and Time = 73 days **

(v) . Principal (P) = Rs 1000

Rate of interest (R) = 10% p.a.

Time (T) = 73 days =\(\frac{73}{365}\)

Simple interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(( \frac{1000\times 10\times\frac{1}{5}}{100})\)

*Q 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 .*

**SOLUTION :**

Principal amount (P) = Rs 500

Time period (T) = 4 years

Rate of interest (R) = 8% p.a.

Interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{500\times 8\times 4}{100} \right )\)

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

*Q 3 . A sum of Rs . 400 is lent at the rate of 5% per annum . Find the interest at the end of 2 years .*

**SOLUTION :**

Principal amount (P) = Rs 400

Time period (T) = 2 years

Rate of interest (R) = 5% p.a.

Interest paid after 2 years = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{400\times 5\times 2}{100} \right )\)

** Q 4** .

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

Principal amount (P) = Rs 400

Time period (T) = 3 years

Rate of interest (R) = 6% p.a.

Interest after 3 years = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{400\times 6\times 3}{100} \right )\)

*Â Q 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 .*

**SOLUTION :**

Principal amount (P) = Rs 25000

Time period (T) = 1 year

Rate of interest (R) = 20% p.a.

Annual interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{25000\times 20\times 1}{100} \right )\)

*Q 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 .*

**SOLUTION :**

Principal amount (P) = Rs 8000

Time period (T) = \(4\frac{1}{2}\)

Rate of interest (R) = 8% p.a.

Interest = \( ( \frac{8000\times 8\times\frac{9}{2}}{100})\)

= 36 x 80 = Rs 2880

Total amount paid afterÂ \(4\frac{1}{2}\)

**Q 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 ?**

**SOLUTION :**

Principal amount lent out by Rakesh (P) = Rs 8000

Time period (T) = 5 years

Rate of interest (R) = 15% p.a.

Interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{8000\times 15\times 5}{100} \right )\)

Principal amount borrowed by Rakesh (P) = Rs 6000

Time period (T) = 3 years

Rate of interest (R) = 12% p.a.

Interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{6000\times 12\times 3}{100} \right )\)

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

*Q 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 1 year ?*

**SOLUTION :**

Principal amount (P) = Rs 1000

Time period (T) = 1 year

Rate of interest (R) = 5% p.a.

Interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{1000\times 5\times 1}{100} \right )\)

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

*Q 9 . Nalini borrowed Rs . 550 from her friend at 8% per annum . She returned the amount after six months . How much did she pay ?*

**SOLUTION :**

Principal amount (P) = Rs 550

Time period (T) = 6 months = \(\frac{1}{2}\)

Rate of interest (R) = 8% p.a.

Interest =Â \(\left ( \frac{P\times R\times T}{100} \right )\)

=Â \((\frac{550\times 8\times\frac{1}{2}}{100})\)

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

*Q 10 . Rohit borrowed Rs . 60000 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 ? *

**SOLUTION :**

Principal amount lent out by Rohit (P) = Rs. 60000

Time period (T) = 2 years

Rate of interest (R) = 10% p.a.

Interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{60000\times 10\times 2}{100} \right )\)

= 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 = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{60000\times 9\times 2}{100} \right )\)

= Rs. 10800

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

*Q 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 watch ?*

**SOLUTION :**

Principal amount borrowed by Romesh (P) = Rs. 2000

Time period (T) = 2 years

Rate of interest (R) = 2% p.a.

Interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{2000\times 2\times 2}{100} \right )\)

Principal amount borrowed by Romesh (P) = Rs. 1000

Time period (T) = 2 years

Rate of interest (R) = 5% p.a.

Interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{1000\times 5\times 2}{100} \right )\)

= 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

*Q 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 ?*

**SOLUTION :**

Principal amount (P) = Rs 12500

Time period (T) = 3 years

Rate of interest (R) = 15% p.a.

Interest = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{12500\times 15\times 3}{100} \right )\)

Rest of the amount lent = Rs 15000 – Rs 12500 = Rs 2500

Rate of interest = 18 % p.a.

Time period = 3 years

Interest =\(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{2500\times 18\times 3}{100} \right )\)

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

*Q 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 ?Â *

**SOLUTION :**

Principal amount deposited (P) = Rs 2000

Time period (T) = 1 year

Rate of interest (R) = 6% p.a.

Interest after 1 year = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{2000\times 6\times 1}{100} \right )\)

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 = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{1420\times 6\times 2}{100} \right )\)

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

*Q 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 ? *

**SOLUTION :**

Principal amount (P) = Rs 8,000

Rate of interest (R) = 18%

Time period (7) = 2 years

Interest after 2 years =Â \(\left ( \frac{P\times R\times T}{100} \right )\)

=Â \(\left ( \frac{8000\times 18\times 2}{100} \right )\)

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

*Q 15 . Mr . Sharma deposited Rs. 20000 as a fixed deposit in a bank at 10% per annum . If 30% is deducted as income tax on the interest earned , find his annual income . *

**SOLUTION :**

Amount deposit (P) = Rs 20,000

Rate of interest (R) = 10% p.a.

Time period (T) = 1 year

Interest after 1 year = \(\left ( \frac{P\times R\times T}{100} \right )\)

= \(\left ( \frac{20000\times 10\times 1}{100} \right )\)

Amount deducted as income tax = 30% of Rs 2,000 = 30 x \(\frac{2000}{100}\)

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