Exercise 2.4 (Simple Interest)

Exercise 2.4

1. Find the simple interest on ₹ 35,000 at 9% per annum for 2 years?

Solution:

Principal P = ₹ 35,000

Rate of interest r = 9% per annum

Time (n) = 2 years

Simple Interest I = Pnr / 100 = (35000 × 2 × 9) / 100 = ₹ 6300

Simple interest I = ₹ 6300

2. Aravind borrowed a sum of ₹ 8,000 from Akash at 7% per annum. Find the interest and amount to be paid at the end of two years.

Solution:

Here Principal P = ₹ 8,000

Rate of interest r = 7% per annum

Time (n) = 2 years

Simple Interest (I) = Pnr / 100 = ( 8000 × 2 × 7) / 100

I = ₹ 1120

Amount = P + I

I = ₹ 8000 + 1120 = 9120

Interest to be paid = ₹ 1,120

Amount to be paid = ₹ 9120

3. Sheela has paid simple interest on a certain sum for 4 years at 9.5% per annum is ₹ 21,280. Find the sum.

Solution:  Let the Principal be ₹ P

Rate of interest r = 9.5% per annum

Time (n) = 4 years

Simple Interest I = Pnr / 100

Given I = ₹ 21,280

∴ Pnr / 100 = ₹ 21,280

[P × 4 × 95] / 100 = ₹ 21,280

[P × 4 × 95] / 1000 = ₹ 21,280

P = (21280 × 1000) / 4 × 95 = ₹ 56,000

∴ Sum of money Sheela bought = ₹ 56,000

4. Basha borrowed ₹ 8,500 from a bank at a particular rate of simple interest. After 3 years, he paid ₹ 11,050 to settle his debt. At what rate of interest he borrowed the money?

Solution:

Let the rate of interest be r% per annum

Here Principal P = ₹ 8500

Time n = 3 years

Total amount paid = ₹ 11,050

A = P + I = ₹ 11,050

i.e. 8,500 + 1 = ₹ 11,050

1 = ₹ 11,050 – ₹ 8,500 = ₹ 2,550

Also we know that I = Pnr / 100 = ₹ 2,550

[ 8,500 × 3 × r ] / 100 = ₹ 2,550

r = (2,550 × 100) / (8500 × 3)

r = 10%

Rate of interest r = 10%

5. In What time will ₹ 16,500 amount to ₹ 22,935 at 13% per annum?

Solution:

Rate of interest r = 13% per annum

Here Amount A = ₹ 22,935

Principal P = ₹ 16,500

A = P + I

22935 = 16,500 + I

∴ Interest I = 22935 – 16,500 = ₹ 6,435

Simple Interest I = Pnr / 100

6435 = (16500 × n × 13) / 100

n = (6435 × 100) / (16500 × 13)

n = 3 years

Required time n = 3 years

6. In what time will ₹ 17800 amount to ₹ 19936 at 6% per annum?

Solution:

Let the require time be n years

Here Principal P = ₹ 17,800

Rate of interest r = 6% per annum

Amount A = ₹ 19,936

A = P + I

19936 = 17800 + I

19936 – 17800 = I

2136 = I

Simple Interest (I) = Pnr / 100

2136 = [ 17800 × n × 6 ] / 100

n = (2136 × 100) / (17800 × 6)

n = 2 years

Required time = 2 years

7. A sum of ₹ 48,000 was lent out at simple interest and at the end of 2 years and 3 months the total amount was ₹ 55,560. Find the rate of interest per year.

Solution:

Given Principal P = ₹ 48,000

Time n = 2 years 3 months

 = 2 + (3/12) years = 2 + (1/4) years

 = 8/4 + 1/4 years = 9/4 years

Amount A = ₹ 55,660

A = P + I

55660 = 48000 + I

I = 55660 – 48000 = ₹ 7660

∴ Interest for 9/4 years = ₹ 7660

Simple Interest = Pnr / 100

7660 = 48000 × 9/4 ×  r/100

 r = (7660 × 4 × 100) / (9 × 48000) = 7.09% = 7%

Rate of Interest = 7% per annum

8. A principal becomes ₹ 17,000 at the rate of 12% in 3 years. Find the principal.

Solution:

Given the Principal becomes ₹ 17,000

Let the principle initially be P

Rate of Interest r = 12% per annum

Time n = 3 years

According to the problem given I = 17000 – P = [ P × 3 × 12 ] / 100

17000 = (36/100) P + P

17000 = P ( 36/100 + 1 )

17000 = P ( 136 / 100 )

P = (17000 × 100) / 136 = 12,500

∴ Principal P = ₹ 12,500

Objective type Questions.

9. The interest for a principle of ₹ 4,500 which gives an amount of ₹ 5,000 at end of certain period is

(i) ₹ 500

( ii) ₹200

( iii) 20%  

(iv) 15%

[Answer: (i) ₹ 500]

Solution: Interest = Amount – Principle = ₹ 5000 – ₹4500 = ₹ 500 

10. Which among the following is the simple interest for the principle of ₹ 1,000 for one year at the rate of 10% interest per annum?

(i) ₹ 200

( ii) ₹10

( ii) ₹100

( ii) ₹1,000

[Answer: (iii) ₹100]

Solution: Interest = Pnr / 100 = [1000×1×10] / 100 = ₹ 100

11. Which among the following rate of interest yields an interest of ₹ 200 for the principle of ₹ 2,000 for one year.

(i) 10%  

(ii) 20%

(iii) 5%

(iv) 15%

[Answer: (i) 10%]

Solution : r = [I × 100] / [P × n] = [200 × 100] / [2000 × 1] = 10% 

ANSWERS:

Exercise 2.4

1. ₹ 6,300

2. I= ₹ 1,120 ; A = ₹ 9,120

3. ₹ 56,000

 4. 10%

5. 3 years

6. 2 years

7. 7%

8. ₹ 12,500

 Objective type questions

9. (i) ₹ 500

10. (iii) ₹ 100

11. (i) 10%