**Download NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.3 – Comparing Quantities**

**NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.3 – Comparing Quantities, has been designed by the NCERT to test the knowledge of the student on the following topics:-**

- Compound Interest
- Deducing a Formula for Compound Interest
- Rate Compounded Annually or Half Yearly (Semi Annually)
- Applications of Compound Interest Formula

**Q.1 Calculate the amount and compound interest on**

**(a) Rs. 10,800 for 3 years at % ****per annum compounded annually.
**

**(b) Rs. 18,000 for**

**years at 10% per annum compounded annually.**

**(c) Rs. 62,500 for**

**years at 8% per annum compounded half yearly.**

**(d) Rs. 8,000 for 1 year at 9% per annum compounded half yearly.**

**(e) Rs. 10,000 for 1 year at 8% per annum compounded half yearly.**

**Solution:**

**(a)** Principal (P) = Rs. 10,800

Rate of interest (R) = % = %

Number of years (n) = 3 [ Time Period ]

Amount (A) =

A =

A =

A = Rs. 15377.3

Compound interest ( C.I ) = A – P = 15377.3 – 10800 = Rs. 4,577.3

**(b)** Principal (P) = Rs. 18,000

Rate of interest (R) = 10%

Number of years (n) = [ Time Period ]

As the Time period is two and half years, Amount is calculated by first calculating the amount for 2 years using the compound interest formula, and then calculating the simple interest for 6 months on the amount obtained at the end of 2 years

Amount for two years:

(A) =

A =

A = 21780

Interest for first two years is A – P = 21780 – 18000 = 3780

Now taking Rs. 21780 as the principal, Simple Interest for next 6 months has to be calculated:

S.I. =

=

= 1089

Interest for next 6 months = Rs. 1089

Therefore, total compound Interest = 3780 + 1089 = 4869

A = 18,000 + 4869 = Rs. 22,869

**(c)** Principal (P) = Rs. 62,500

Rate of interest (R) = 8% = 4% per half year

Number of years (n) = [ Time Period ]

As the interest is calculated half yearly, there are three half years in years

(A) =

A =

A = Rs. 70304

Compound Interest (C.I.) = 70304 – 62500=Rs. 7,804

**(d)** Principal (P) = Rs. 8000

Rate of interest (R) = 9% = % per half year

Number of years (n) = 1 [ Time Period ]

As the interest is calculated half yearly, there are two half years in year

(A) =

A =

A = Rs. 8736.20

Compound Interest (C.I.) = 8736.20 – 8000 = Rs. 736.20

**(e)** Principal (P) = Rs. 10000

Rate of interest (R) = 8% = 4% per half year

Number of years (n) = 1 [ Time Period ]

As the interest is calculated half yearly, there are two half years in year

(A) =

A =

A = Rs. 10,816

Compound Interest (C.I.) = 10816 – 10000 = Rs. 816

**Q.2 ****Kamala borrowed Rs 26400 from a Bank to buy a scooter at a rate of 15% p.a.** **compounded yearly. What amount will she pay at the end of 2 years and 4 months** **to clear the loan? **

**(Hint: Find A for 2 years with interest is compounded yearly and then find SI on the 2 ^{nd} year amount for 4/12 years)**

**Solution:**

Given, Kamala borrowed Rs 26400 from a Bank to buy a scooter at a rate of 15% per annum compounded yearly

Principal (P) = Rs 26,400

Rate of interest (R) = 15% per annum

Number of years (n) = years

As the time period is Two years and Four months, the amount is calculated by first calculating the amount for 2 years using the compound interest and then calculating the simple interest for 4 months on the amount obtained for the first two years

Amount for two years:

(A) =

A =

A = Rs. 34914

Interest for the first two years = 34914 − 26400 = Rs. 8514

Now taking Rs. 34914 as the principal, simple interest for next 4 months has to be calculated:

S.I. =

S.I, =

S.I. = 1745.70

Interest for next 4 months = Rs. 1745.70

Therefore, Total C.I. = 8514 + 1745.70 = Rs. 10,259.70

Amount = P + C.I. = 26400 + 10259.70 = Rs. 36,659.70

Therefore, Kamala would pay Rs. 36,659.70 at the end of years and 4 months to clear the loan

**Q.3. Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much? **

**Solution:**

Given, Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually

Interest paid by Fabina (S.I.) =

12500 x 3 x = Rs. 4500

Interest paid by Radha (C.I) = – P

= – 12500

= 16637.50 – 12500 = Rs. 4137.50

Interest paid bt Fabina is Rs. 4500 whereas interest paid by Radha is Rs. 4137.50

Therefore, Fabina pays more interest

4500 – 4137.50 = Rs. 362.50

**Q.4 I borrowed Rs 12000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?**

**Solution:**

Given, I borrowed Rs. 12000 from Jamshed at 6% p.a. simple interest for 2 years

Principal (P) = Rs. 12000

Rate of interest (R) = 6% per annum

Time = 2 years

Simple Interest (S.I.) =

= 12000 x 2 x = Rs. 1440

Compound Interest (C.I.) = – P

– 12000

= 13483.20 – 12000

= Rs. 1483.20

C.I. = Rs. 1,483.20

S.I. = Rs. 1,440.00

C.I. – S.I. = Rs. 1,483.20 – Rs. 1,440.00 = Rs. 43.20

Therefore, the extra amount to be paid is Rs. 43.20

**Q.5 Vasudevan invested Rs 60000 at an interest rate of 12% per annum compounded half yearly. What amount would he get
**

**(i) after 6 months?**

(ii) after 1 year?

(ii) after 1 year?

**Solution:**

Given, Vasudevan invested Rs 60000 at an interest rate of 12% per annum compounded half yearly

**(i)** Principal (P) = Rs. 60000

Rate of interest = 12% per annum = 6% per half year

Time (n) = 6 months (1 half year )

A =

A =

A = 63600

Therefore, the amount Vasudevan would get after 6 months is Rs. 63600

**(ii)** Principal (P) = Rs. 60000

Rate of interest = 12% per annum = 6% per half year

Time (n) = 12 months (2 half years )

A =

A =

A = 67416

Therefore, the amount Vasudevan would get after 12 months is Rs. 67416

**Q.6 Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after **** ****years if the interest is **

**(i) Compounded annually
**

**(ii) Compounded half yearly**

** ****Solution:**

Given, Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum

**(i)** Principal (P) = Rs 80000

Rate of interest = 10% per annum

Time (n) = years

As the time period is 1 year and 6 months, the amount can be calculated by first calculating the amount for 1 year using the compound interest, and then calculating the simple interest for 6 months on the amount obtained at the end of 1 year.

Amount for 1 year:

A =

A =

A = Rs. 88000

Interest for the first 1 year = 88000 – 80000 = Rs. 8000

Now taking Pricipal (P) as Rs. 88000, Simple interest for next 6 months has to be calculated:

S.I. =

S.I. =

S.I. = Rs. 4400

Interest for next 6 months = Rs. 4400

Total Compound Interest (C.I.) = 8000 + 4400 = Rs. 12400

Total Amount (A) = P + C.I. = 80000 + 12400 = Rs. 92400

**(ii)** interest is compounded half yearly

Principal (P) = Rs 80000

Rate of interest = 10% per annum = 5% per half year

Time (n) = years ( 3 half years )

A =

A =

A = Rs. 92610

Difference between the amounts that Arif would pay when the interest is compounded half yearly and annually = 92610 – 92400 = Rs. 210

**Q.7 Maria invested Rs. 8000 in a business. She would be paid interest at 5% per annum compounded annually. Find. **

**(i) The amount credited against her name at the end of the second year
**

**(ii) The interest for the 3rd year**

**Solution:**

Given, Maria invested Rs. 8000 in a business. She would be paid interest at 5% per annum compounded annually

**(i)** P = Rs. 8000

R = 5% per annum

n = 2 years

A=

A=

A = Rs. 8820

Amount that would be credited at the end of second year is Rs. 8820

**(ii)** interest for the third year can be calculated by taking Rs. 8820 as principal and calculating the S.I. for the next year

S.I.=

S.I. =

S.I. = Rs. 441

Interest for the third year is Rs. 441

**Q.8 Find the amount and the compound interest on Rs 10,000 for **** years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually? **

**Solution:**

Given,

Principal (P) = Rs. 10000

Rate = 10% per annum = 5% per half year

n = years ( 3 half years )

A=

A=

A = Rs. 11576.25

Compound Interest (C.I.) = A − P = 11576.25 − 10000 = Rs. 1576.25

As the time period is 1 year and 6 months, the amount can be calculated by first calculating the amount for 1 year using the compound interest, and then calculating the simple interest for 6 months on the amount obtained at the end of 1 year.

Amount for 1 year:

A=

A=

A = Rs. 11000

Interest for the first 1 year = 11000 – 10000 = Rs. 1000

Now taking Principal (P) as Rs. 11000, Simple interest for next 6 months has to be calculated:

S.I.=

S.I. =

S.I. = Rs. 550

Interest for next 6 months = Rs. 550

Total Compound Interest (C.I.) = 1000 + 550 = Rs. 1550

1576 > 1550

Therefore, the interest would be more when compounded half yearly than the interest when compounded annually

**Q.9 ****Find the amount which Ram will get on Rs. 4096,he gave it for 18 months at **** % per annum, interest being compounded half yearly. **

**Solution:**

Given,

P = Rs 4,096

R = % per annum = % per half year

n = 18 months ( 3 half years )

A=

A=

A = Rs. 4913

Therefore, Ram will get an amount of Rs. 4913

**Q.10 The population of a place increased to 54000 in 2003 at a rate of 5% per annum **

**(i) find the population in 2001
**

**(ii) what would be its population in 2005?**

**Solution:**

**(i)** Given, population of a place increased to 54000 in 2003 at a rate of 5% per annum.

Let, population be in 2001

54000=

= 54000 x x

= 48979.6

Therefore, the population in 2001 is 48980

**(ii)** Population in 2005:

= 59535

Therefore, the population in 2005 would be 59535

**Q.11 ****In a laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5,06,000. **

**Solution:**

Given,

Rate of bacteria increasing at 2.5% per hour

The initial count of bacteria is 5,06,000.

Bacteria at the end of 2 hours be

=

= 531616.25

Therefore, count of bacteria at the end of 2 hours would be 5,31,616 (approx)

**Q.12 A scooter was bought at Rs 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year. **

**Solution:**

Given, A scooter was bought at Rs 42,000

Its value depreciated at the rate of 8% per annum

Cost price of the scooter = Principal (P) = Rs 42,000

Depreciation = Rate of decrease = 8% per year

Value of scooter after one year:

=

= 3360

Therefore, value of scooter after 1 year = 42000 − 3360 = Rs. 38640

**The next Exercise for** **NCERT Solutions for Class 8 Maths Chapter 9 Exercise 9.1 – Algebraic Expressions and Identities can be accessed by clicking here**

**Download NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.3 – Comparing Quantities**

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