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Textbook | NCERT |

Class | Class 8 |

Subject | Maths |

Chapter | Chapter 14 |

Chapter Name | Compound Interest |

Exercise | Ex 14.1 |

**RD Sharma Solutions for Class 8 Chapter 14 Compound Interest Ex 14.1** **Download PDF**

**Question 1.****Find the compound interest when principal = Rs 3,000, rate = 5% per annum and time = 2 years.****Solution:**

Principal (P) = Rs 3,000

Rate (R) = 5% p.a.

Period (T) = 2 years

Amount after one year = Rs 3,000 + Rs 150 = 3,150

and principal for the second year = Rs 3,150

and interest for the second year

Compound interest for two years = Rs 150 + Rs 157.50 = Rs 307.50

**Question 2.****What will be the compound interest on Rs 4,000 in two years when rate of interest is 5% per annum ?****Solution:**

Principal (P) = Rs 4,000

Rate (R) = 5% p.a.

Period (T) = 2 years

Amount after one year = Rs 4,000 + Rs 200 = Rs 4,200

Principal for the second year = Rs 4,200

Interest for the second year

Compound interest for 2 years = Rs 200 + Rs 210 = Rs 410

**Question 3.****Rohit deposited Rs 8,000 with a finance company for 3 years at an interest of 15% per annum. What is the compound interest that Rohit gets after 3 years ?****Solution:**

Principal (P) = Rs 8,000

Rate (R) = 15% p.a.

Period (T) = 3 years

Amount after first year = Rs 8,000 + RS 1,200 = Rs 9,200

or Principal for the second year = Rs 9,200

Interest for the second year

Amount after 2 years = Rs 9,200 + Rs 1,380 = Rs 10,580

or Principal for the third year = Rs 10,580

Interest for the third year

Compound for the 3 years = Rs 1,200 + Rs 1,380 + Rs 1,587 = Rs 4,167

**Question 4.****Find the compound interest on Rs 1,000 at the rate of 8% per annum for 112 years when interest is compounded half-yearly ?****Solution:**

Principal (P) = Rs 1,000

Rate (R) = 8% p.a.

Period (T) = 112 years = 3 half-years

Amount after one half-year = Rs 1,000 + Rs 40 = 1,040

Or principal for the second half-year = Rs 1,040

Interest for the second half-year

Amount after second half-year = Rs 1,040 + 41.60 = Rs 1,081.60

Or principal for the third half-year = Rs 1081.60

Interest for the third half-year

Compound interest for the third half-years or 112 years

= Rs 40 + Rs 41.60 + Rs 43.264 = Rs 124.864

**Question 5.****Find the compound interest on Rs 1,60,000 for one year at the rate of 20% per annum, if the interest is compounded quarterly.****Solution:**

Principal (P) = Rs 1,60,000

Rate (R) = 20% p.a. or 5% quarterly

Period (T) = 1 year or 4 quarters

Amount after first quarter = Rs 1,60,000 + 8,000 = 1,68,000

Or principal for the second quarter = Rs 1,68,000

Interest for the second quarter

Amount after the second quarter = Rs 1,68,000 + Rs 8,400 = 1,76,400

Or principal for the third quarter = Rs 1,76,400

Interest for the third quarter

Amount after third quarter = Rs 1,76,400 + 8,820 = Rs 1,85,220

or Principal for the fourth quarter = Rs. 1,85,220

Interest for the fourth quarter

Total compound interest for the 4 quarters = Rs 8,000 + Rs 8,400 + Rs 8,820 + 9,261 = Rs 34,481

**Question 6.****Swati took a loan of Rs 16,000 against her insurance policy at the rate of 1212 % per annum. Calculate the total compound interest payable by Swati after 3 years.****Solution:**

Amount of loan or principal (P) = Rs 16,000

Amount after first year = Rs 16,000 + Rs 2,000 = Rs 18,000

Principal for the second year = Rs 18,000

Interest for the second year

Amount after second year = Rs 18,000 + 2,250 = Rs 20,250

Principal for the third year = Rs 20,250

Compound for 3 years = Rs 2,000 + Rs 2,250 + 2531.25 = Rs 6,781.25

**Question 7.****Roma borrowed Rs 64,000 from a bank for 112 years at the rate of 10% per annum. Compute the total compound interest payable by Roma after 112 years, if the interest is compounded half-yearly.****Solution:**

Principal (sum borrowed) (P) = Rs 64,000

Rate (R) = 10% p.a. or 5% half-yearly

Period (T) = 112 years or 3 half-years

Amount after first half-year = Rs 64,000 + Rs 3,200 = Rs 67,200

Or principal for the second half-year = Rs 67,200

Interest for the second half-year

Amount after second half-year = Rs 6,7200 + 3,360 = Rs 70,560

Or principal for the third half-year = Rs 70,560

Interest for the third half-year

Total compound interest for 3 half-years

or 112 years = Rs 3,200 + Rs 3,360 + Rs 3,528 = Rs 10,088

**Question 8.****Mewa Lai borrowed Rs 20,000 from his friend RoopLal at 18% per annum simple interest. He lent it to Rampal at the same rate but compounded annually. Find his gain after 2 years.****Solution:**

Principal (P) = Rs 20,000

Rate (R) = 18% p.a.

Period (T) = 2 years

In second case

Interest for the first year

Amount after one year = Rs 20,000 + Rs 3,600 = Rs 23,600

Or principal for the second year = Rs 23,600

Interest for the second year

Interest for two years = Rs 3,600 + 4,248 = Rs 7,848

Gain = Rs 7,848 – Rs 7,200 = Rs 648

**Question 9.****Find the compound interest on Rs 8,000 for 9 months at 20% per annum compounded quarterly.****Solution:**

Principal (P) = Rs 8,000

Rate (R) = 20% p.a. or 5% p.a. quarterly

Period (T) = 9 months or 3 quarters

Interest for the first quarterly

Amount after first quarter = Rs 8,000 + Rs 400 = Rs 8,400

Or principal for second quarter = Rs 8,400

Interest for the second quarter

Amount after second quarter = Rs 8,400 + Rs 420 = Rs 8,820

Or principal for the third quarter = Rs 8,820

Interest for the third quarter

Compound interest for 9 months or 3 quarters = Rs 400 + Rs 420 + Rs 441 = Rs 1,261

**Question 10.****Find the compound interest at the rate of 10% per annum for two years on that principal which in two years at the rate of 10% per annum gives Rs. 200 as simple interest.****Solution:**

Simple interest = Rs 200

Rate (R) = 10% p.a.

Period (T) = 2 years.

Now in second case,

Principal CP) = Rs 1,000

Rate (R) = 10% p.a.

Period (T) = 2 years.

Amount after one year = Rs 1,000+ Rs 100 = Rs 1,100

Or principal for the second year = Rs 1,100

Total interest for two years = Rs 100 + Rs 110 = Rs 210

**Question 11.****Find the compound interest on Rs 64,000 for 1 year at the rate of 10% per annum compounded quarterly.****Solution:**

Principal (P) = Rs 64,000

Rate (R) = 10% p.a. or 52 % quarterly

Period (T) = 1 year = 4 quarters

Amount after first quarter = Rs 64,000 + Rs 1,600 = Rs 65,600

Or principal for the second quarter = Rs 65,600

Interest for the second quarter

Amount after second quarter = Rs 65,600 + Rs 1,640 = Rs 67,240

Or principal for the third year = Rs 67,240

= Rs 1,681

Amount after third quarter = Rs 67,240 + Rs 1,681 = Rs 68,921

Or principal for the fourth quarter

Total compound interest for 4 quarters or one year

= Rs 1,600 + Rs 1,640 + Rs 1,681 + Rs 1723.025 = Rs 6644.025

**Question 12.****Ramesh deposited Rs 7,500 in a bank which pays him 12% interest per annum compounded quarterly. What is the amount which he receives after 9 months ?****Solution:**

Principal (P) = Rs 7,500

Rate (R) = 12% p.a. or 3% quarterly

Time (T) = 9 months or 3 quarters

Amount after one quarter = Rs 7,500 + Rs 225 = Rs 7,725

Or Principal for second quarter = Rs 7,725

Interest for the second quarter

Amount after second quarter = Rs 7,725 + Rs 231.75 = Rs 7956.75

Or principal for the third quarter

Total amount he received after 9 months = Rs 7956.75 + Rs 238.70 = Rs 8195.45

**Question 13.****Anil borrowed a sum of Rs 9,600 to install a hand pump in his dairy. If the rate of interest is 512 % .per annum compounded annually, determine the compound interest which Anil will have to pay after 3 years.****Solution:**

Principal (P) = Rs 9,600

Rate of interest (R) = 512 % = 112 % p.a.

Period (T) = 3 years.

Amount after one year = Rs 9,600 + Rs 528 = Rs 10,128

Or principal for second year = Rs 10,128

Interest for the second year

Amount after second year = Rs 10,128 + Rs 557.04 = Rs 10685.04

or Principal for the third year = Rs 10685.04

Interest for the third year

Total compound interest = Rs 528 + Rs 557.04 + Rs 587.68 = Rs 1672.72

**Question 14.****Surabhi borrowed a sum of Rs 12,000 from a finance company to purchase a refrigerator. If the rate of interest is 5% per annum compounded annually, calculate the compound interest that Surabhi has to pay to the company after 3 years.****Solution:**

Sum of money borrowed (P) = Rs 12,000

Rate (R) = 5% p.a.

Period (T) = 3 years

Amount after one year = Rs 12,000 + Rs 600 = Rs 12,600

Or principal for the second year = Rs 12,600

Interest for the second year

Amount after second year = Rs 12,600 + Rs 630 = Rs 13,230

Or Principal for the third year = Rs 13,230

Interest for the third year

Total compound interest for 3 years = Rs 600 + Rs 630 + Rs 661.50 = Rs 1891.50

**Question 15.****Daljit received a sum of Rs 40,000 as a loan from a finance company. If the rate of interest is 7% per annum compounded annually, calculate the compound interest that Daljit pays after 2 years.****Solution:**

Amount of loan (P) = Rs 40,000

Rate (R) = 7% p.a.

Period = 2 years

Amount after one year = Rs 40,000 + Rs 2,800 = Rs 42,800

Or principal for the second year = Rs 42,800

Interest for the second year

Total interest paid after two years = Rs 2,800 + 2,996 = Rs 5,796

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