# Comparing Quantities : Exercise 8.3 (Mathematics NCERT Class 8th)

**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. (You could use the year by year calculation using SI formula to verify).**

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

**(a) Here, principal (P) = Rs 10,800, Rate(R) = % = % (annual), Number of years (n) = 3.**

*Sol.*Amount, A =

= Rs

= Rs

= Rs

= Rs 15377.34

Compound Interest, C.I. = A â€“ P = Rs (15377.34 â€“ 10800) = Rs 4,577.34

(b) Here, principal (P) = Rs 18,000, Rate(R) = %, Number of years (n) = years.

Calculation for first 2 years:

Amount, A =

= Rs

= Rs

= Rs 21,780

Calculation for next 6 months:

S.I. = Rs = Rs 1089

Therefore, interest for the first two years = Rs (21780 - 18000) = Rs 3780

And interest for next year = Rs 1,089

Hence, total C.I. = Rs 18000 + Rs 4869 = Rs 22,869

(c) Here, principal (P) = Rs 62,500, Rate(R) = 8% per annum or 4% per half year, Number of years (n) = .

Amount, A =

= Rs

= Rs

= Rs 70304

Compound Interest, C.I. = A â€“ P = Rs (70304 â€“ 62500) = Rs 7,804

(d) Here, principal (P) = Rs 8,000, Rate(R) = 9% per annum or % per half year, Number of years (n) = 1.

Amount, A =

= Rs

= Rs

= Rs 8736.20

Compound Interest, C.I. = A â€“ P = Rs (8736.20 â€“ 8000) = Rs 736.20

(e) Here, principal (P) = Rs 10,000, Rate(R) = 8% per annum or 4% per half year, Number of years (n) =1.

We know that, there are 2 half years in 1 year.

Amount, A =

= Rs

= Rs

= Rs 10,816

Compound Interest, C.I. = A â€“ P = Rs (10816 â€“ 10000) = Rs 816

**Q.2 Kamala borrowed Rs 26,400 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 2nd year amount for ****years).
**

**Here, principal (P) = Rs 26,400, Rate(R) = 15% per annum, Number of years (n) =years.**

*Sol.*Calculation for first 2 years:

Amount, A =

= Rs

= Rs

= Rs 34,914

Calculation for next years:

S.I. = Rs= Rs 1,745.70

Now, interest for the first two years = Rs (34914 â€“ 26400) = Rs 8,514

And interest for the next year = Rs 1,745.70

Total C.I. = Rs (8514 + 1745.70) = Rs 10,259

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

**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?
**

**Here, principal (P) = Rs 12,500, Rate(R) = 12% per annum, Number of years (n) =3 years.**

*Sol.*S. I. for Fabina = = = Rs 4500

For Radha:

Principal (P) = Rs 12,500, Rate(R) = 10% per annum, Number of years (n) =3 years

Amount, A =

=

=

=

= Rs 16,637.50

Compound Interest, C.I. = A â€“ P = Rs (16637.50 â€“ 12500) =Rs 4,137.50

The difference between Fabinaâ€™s and Radhaâ€™s interest = Rs (4500 â€“ 4137.50) = Rs 362.50

Therefore, Fabina will have to pay Rs 362.50 more.

**Q.4 I borrowed Rs 12,000 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?
**

**Here, principal (P) = Rs 12,000, Rate(R) = 6% per annum, Number of years (n) =2 years.**

*Sol.*S. I. = = = Rs 1,440

Calculation for Compound Interest (C.I.):

Amount, A =

=

=

=

= Rs 13,483.20

Therefore, Compound Interest = A â€“ P = Rs 13483.20 â€“ Rs 12000 = Rs 1,483.20

Now, C.I. â€“ S.I. = Rs 1,483.20 â€“ Rs 1,440 = Rs 43.20

Therefore, extra amount to be paid is Rs 43.20

**Q.5 Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compounded half yearly. What amount would he get
**

**(i) after 6 months?**

**(ii) after 1 year?**

**(i) Here, principal (P) = Rs 60,000, Rate(R) = 12% per annum = 6% per half year, Number of years (n) =6 months = 1 half year.**

*Sol.*Amount, A =

=Rs

= Rs

= Rs 63,600

(ii) We know that, 2 half years in 1 year. Therefore, n = 2.

A =Rs

= Rs

= Rs 67,416

**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.**

**(i) Here, principal (P) = Rs 80,000, Rate(R) = 10% per annum, Number of years (n) =6 months = half year.**

*Sol.*Calculation for 1

^{st}year:

Amount, A =

=Rs

= Rs

= Rs 88,000

Calculation for next year taking Rs 88,000 as principal:

S.I. = = Rs = Rs 4,400

Now, interest for next first year = Rs 88,000 â€“ Rs 80,000 = Rs 8,000

And interest for next year = Rs 4,400

Here, C.I. = Rs 8,000 + Rs 4,4000 = Rs 12,400

Hence, Total C.I. = Rs (80000 + 12400) = Rs 92,400

(ii) For the interest compounded half yearly:

Rate(R) = 10% per annum = 5% per half yearly.

There will be three half years in years.

Amount, A =

A = Rs

= Rs

= Rs 92,610

Thus, the difference between amounts = Rs 92,610 â€“ Rs 92,400 = Rs 210

**Q.7 Maria invested Rs 8,000 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**

**(i) Here, principal (P) = Rs 8,000, Rate(R) = 5% per annum, Number of years (n) =2 years.**

*Sol.*Amount, A =

A = Rs

= Rs

= Rs 8,820

(ii) Now, calculating S.I. for next year taking Rs 8,820

S.I. = Rs = 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?
**

**Here, principal (P) = Rs 10,000, Rate(R) = 10% per annum = 5% per half year, Number of years (n) = years.**

*Sol.*In there will be 3 half years.

Amount, A =

A = Rs

= Rs

= Rs 11,576.25

Now, Compound Interest C.I. = A â€“ P

= Rs 11576.25 â€“ Rs 10000

= Rs 1,576.25

Now, calculating amount for the first year

Amount, A =

A = Rs

= Rs

= Rs 11,000

Now, taking Rs 11,000 as principal, S.I. for next half year will be:

S.I. =

= Rs 550

Hence, interest for the first year = Rs 11000 â€“ Rs 10000 = Rs 1000

Therefore, Compound Interest C.I. = Rs 1000 + Rs 550 = Rs 1,550

Thus, the interest would be more when compounded half year as compared to the interest when compounded annually.

**Q.9 Find the amount which Ram will get on Rs 4096, if he gave it for 18 months at ****% 2 per annum, interest being compounded half yearly.
**

**Here, principal (P) = Rs 4,096, Rate(R) = % per annum = % per half year, Number of months = 18.**

*Sol.*In 18 months, there will be 3 half years, therefore,

Amount, A =

A = Rs

= Rs

= Rs 4,913

Therefore, the required amount is Rs 4,913.

**Q.10 The population of a place increased to 54,000 in 2003 at a rate of 5% per annum
**

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

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

**(i) Given, population in 2003 = 54,000.**

*Sol.*Hence, 54000 = Population in 2001 x

Population in 2001=

= Rs 48979.59

Hence, the population in the year 2001 was approximately 48,980.

(ii) Population in 2005 = 54000 x

=

= 59,535

Hence, the population in the year 2005 would be 59,535.

**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.
**

**Given, the initial count of bacteria is 5,06,000.**

*Sol.*Now, bacteria at the end of 2 hours = 506000 x

=

= 5,31,616.25

Hence, the count of bacteria at the end of 2 hours will be approximately 5,31,616

**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.
**

**Here, principal (P) = Rs 42,000, rate = 8% per annum**

*Sol.*Depreciation = *% of Rs 42,000 per year

= Rs

= Rs 3,360

Therefore, value after one year = Rs 42000 â€“ Rs 3360 = Rs 38,640

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