## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 8 Simple and Compound Interest Ex 8.2

Question 1.

Calculate the compound interest on ₹6000 at 10% per annum for two years.

Solution:

Rate of interest = 10% per annum

Principal for the first year = ₹6000

Interest for the first year = ₹\(\frac{6000 \times 10 \times 1}{100}\) = ₹6000

Amount at the end of first year = ₹6000 + ₹600 = ₹6600

Principal for the 2nd year = ₹6600

Interest for the 2nd year = ₹\(\frac{6600 \times 10 \times 1}{100}\) = ₹660

Amount for the second year = ₹6600 + ₹660 = ₹7260

∴ Compound interest for 2 years = final amount – (original) Principal

= ₹ 7260 – ₹6000 = ₹1260

Question 2.

Salma borrowed from Mahila Samiti a sum of ₹ 1875 to purchase a sewing machine. If the rate of interest is 4% per annum, what is the compound interest that she has to pay after 2 years?

Solution:

Principal for the 1st year = ₹1875

Rate of’interest = 4% p.a.

Interest for the 1st year = ₹ \(\frac{6000 \times 10 \times 1}{100}\) = ₹600

Amount at the end of first year = ₹1875 + ₹75 = ₹1950

Principal for the 2nd year = ₹1950

Interest for the 2nd year = ₹ \(\frac{6000 \times 10 \times 1}{100}\) = ₹600

Amount at the end of 2nd year = ₹1950 + ₹78 = ₹2028

∴ Compound interest paid by Salma

= Final amount – (original) Principal

= ₹2028 – ₹1875 = ₹153

Question 3.

Jacob invests ₹12000 for 3 years at 10% per annum. Calculate the amount and the compound interest that Jacob will get after 3 years.

Solution:

Principal for the 1st year = ₹ 12000

Rate = 10% p.a.

Interest for the 1st year = ₹ \(\frac{12000 \times 10 \times 1}{100}\) = ₹1200

Amount at the end of 1 st year = ₹12000 + ₹1200 = ₹13200

Principal for the 2nd year = ₹ 13200

Interest for the 2nd year = ₹ \(\frac{13200 \times 10 \times 1}{100}\) = ₹ 1320

Amount at the end of 2nd year = ₹13200 + ₹1320 = ₹14520

Principal for the 3rd year = ₹ 14520

Interest for the 3rd year = ₹ \(\frac{14520 \times 10 \times 1}{100}\) = ₹1452

Amount at the end of 3rd year = ₹14520 + ₹1452 = ₹15972

Compound interest for 3 year=Final amount – (original) Principal

= ₹15972 – ₹12000 = ₹3972

Question 4.

A man invests ₹46875 at 4% per annum compound interest for 3 years.

Calculate:

(i) the interest for the first year.

(ii) the amount standing to his credit at the end of the second year.

(iii) the interest for the third year.

Solution:

(i) Principal for the 1st year = ₹46875

Rate = 4% per annum

∴ Interest for the 1st year

(ii) Amount at the end of 1st year

= ₹46875 + ₹1875 = ₹48750

Principal for the 2nd year = ₹48750

Interest for the 2nd year

Amount at the end of 2nd year

= ₹48750 + ₹1950 = ₹50700

(iii) Principal for the 3rd year = ₹50700

Interest for the 3rd year = ₹\(\frac{50700 \times 4 \times 1}{100}\)

= ₹507 × 4 = ₹2028

Question 5.

Calculate the compound interest for the second year on ₹6000 invested for 3 years at 10% p.a. Also find the sum due at the end of third year.

Solution:

Principal for the 1st year = ₹6000

Rate = 10% p.a.

Interest for the 1st year = ₹\(\frac{6000 \times 10 \times 1}{100}\) = ₹600

Amount at the end of 1st year = ₹6000 + ₹600 = ₹6600

Principal for the 2nd year = ₹6600

Interest for the 2nd year = ₹ \(\frac{6600 \times 10 \times 1}{100}\) = ₹660

Amount at the end of 2nd year = ₹6600 + ₹660 = ₹7260

Compound interest for the 2nd year

= Final amount – (original) Principal

= ₹7260 – ₹6000 = ₹1260

Principal for the 3rd year = ₹7260

Interest for the 3rd year = ₹ \(\frac{7260 \times 10 \times 1}{100}\) = ₹726

Amount at the end of 3rd year = ₹7260 + ₹726 = ₹7986

Question 6.

Calculate the amount and the compound interest on ₹5000 in 2 years when the rate of interest for successive years is 6% and 8% respectively.

Solution:

Principal for the 1st year = ₹5000

Rate = 6% p.a.

Interest for the 1st year = ₹ \(\frac{5000 \times 6 \times 1}{100}\)

= ₹50 × 6 × 1 = ₹300

Amount at the end of 1st year = ₹5000 + ₹300 = ₹5300

Principal for the 2nd year = ₹5300

Rate = 8% p.a.

Interest for the 2nd year = ₹ \(\frac{5300 \times 8 \times 1}{100}\)

= ₹53 × 8 = ₹424

Amount for the 2nd year = ₹5300 + ₹424 = ₹5724

Compound interest for two years = Final amount – (original) Principal

= ₹5724 – ₹5000 = ₹724

Question 7.

Calculate the difference between the compound interest and the simple interest on ₹20000 in 2 years at 8% per annum.

Solution:

Principal (P) = ₹20000

Rate (R) = 8% p.a.

Period (T) = 2 years

= ₹32 × 729 = ₹23328

∴ Compound interest = A – P

= ₹23328 – 20000 = ₹3328 .

∴ Difference in C.I. and S.I.

= ₹3328 – ₹3200 = ₹128