Simple and Compound Interest — Exercise 8.2

Calculate the compound interest on ₹6,000 at 10% per annum for two years.

Answer

Given:

Principal (P) = ₹ 6,000

Rate of interest (R) = 10% p.a.

Time (T) = 2 years

Principal for the first year = ₹ 6,000

$\Rightarrow \text{Interest for the first year} = ₹ \dfrac{6000 \times 10 \times 1}{100} = ₹ 600$

Amount at the end of first year = ₹ 6,000 + ₹ 600 = ₹ 6,600

Principal for the second year = ₹ 6,600

$\Rightarrow \text{Interest for the second year} = ₹ \dfrac{6600 \times 10 \times 1}{100} = ₹ 660$

Amount at the end of second year = ₹ 6,600 + ₹ 660 = ₹ 7,260

Compound interest = Final amount - Original principal

= ₹ 7,260 - ₹ 6,000

= ₹ 1,260

Hence, the compound interest on ₹ 6,000 for two years = ₹ 1,260.

Salma borrowed a sum of ₹9,375 from a local self-help group 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?

Answer

Given:

Principal (P) = ₹ 9,375

Rate of interest (R) = 4% p.a.

Time (T) = 2 years

Principal for the first year = ₹ 9,375

$\Rightarrow \text{Interest for the first year} = ₹ \dfrac{9375 \times 4 \times 1}{100} = ₹ 375$

Amount at the end of first year = ₹ 9,375 + ₹ 375 = ₹ 9,750

Principal for the second year = ₹ 9,750

$\Rightarrow \text{Interest for the second year} = ₹ \dfrac{9750 \times 4 \times 1}{100} = ₹ 390$

Amount at the end of second year = ₹ 9,750 + ₹ 390 = ₹ 10,140

Compound interest = Final amount - Original principal

= ₹ 10,140 - ₹ 9,375

= ₹ 765

Hence, the compound interest that Salma has to pay after 2 years = ₹ 765.

Jacob invests ₹12,000 for 3 years at 10% per annum. Calculate the amount and the compound interest that Jacob will get after 3 years.

Answer

Given:

Principal (P) = ₹ 12,000

Rate of interest (R) = 10% p.a.

Time (T) = 3 years

Principal for the first year = ₹ 12,000

$\Rightarrow \text{Interest for the first year} = ₹ \dfrac{12000 \times 10 \times 1}{100} = ₹ 1{,}200$

Amount at the end of first year = ₹ 12,000 + ₹ 1,200 = ₹ 13,200

Principal for the second year = ₹ 13,200

$\Rightarrow \text{Interest for the second year} = ₹ \dfrac{13200 \times 10 \times 1}{100} = ₹ 1{,}320$

Amount at the end of second year = ₹ 13,200 + ₹ 1,320 = ₹ 14,520

Principal for the third year = ₹ 14,520

$\Rightarrow \text{Interest for the third year} = ₹ \dfrac{14520 \times 10 \times 1}{100} = ₹ 1{,}452$

Amount at the end of third year = ₹ 14,520 + ₹ 1,452 = ₹ 15,972

Compound interest = Final amount - Original principal

= ₹ 15,972 - ₹ 12,000

= ₹ 3,972

Hence, the amount = ₹ 15,972 and the compound interest = ₹ 3,972.

A man invests ₹46,875 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 second year.

(iii) the interest for the third year.

Answer

Given:

Principal (P) = ₹ 46,875

Rate of interest (R) = 4% p.a.

Time (T) = 3 years

(i) Principal for the first year = ₹ 46,875

$\Rightarrow \text{Interest for the first year} = ₹ \dfrac{46875 \times 4 \times 1}{100} = ₹ 1{,}875$

Hence, the interest for the first year = ₹ 1,875.

(ii) Amount at the end of first year = ₹ 46,875 + ₹ 1,875 = ₹ 48,750

Principal for the second year = ₹ 48,750

$\Rightarrow \text{Interest for the second year} = ₹ \dfrac{48750 \times 4 \times 1}{100} = ₹ 1{,}950$

Amount at the end of second year = ₹ 48,750 + ₹ 1,950 = ₹ 50,700

Hence, the amount standing to his credit at the end of second year = ₹ 50,700.

(iii) Principal for the third year = ₹ 50,700

$\Rightarrow \text{Interest for the third year} = ₹ \dfrac{50700 \times 4 \times 1}{100} = ₹ 2{,}028$

Hence, the interest for the third year = ₹ 2,028.

Calculate the compound interest for the second year on ₹6,000 invested for 3 years at 10% p.a. Also find the sum due at the end of third year.

Answer

Given:

Principal (P) = ₹ 6,000

Rate of interest (R) = 10% p.a.

Time (T) = 3 years

Principal for the first year = ₹ 6,000

$\Rightarrow \text{Interest for the first year} = ₹ \dfrac{6000 \times 10 \times 1}{100} = ₹ 600$

Amount at the end of first year = ₹ 6,000 + ₹ 600 = ₹ 6,600

Principal for the second year = ₹ 6,600

$\Rightarrow \text{Interest for the second year} = ₹ \dfrac{6600 \times 10 \times 1}{100} = ₹ 660$

Amount at the end of second year = ₹ 6,600 + ₹ 660 = ₹ 7,260

Principal for the third year = ₹ 7,260

$\Rightarrow \text{Interest for the third year} = ₹ \dfrac{7260 \times 10 \times 1}{100} = ₹ 726$

Amount at the end of third year = ₹ 7,260 + ₹ 726 = ₹ 7,986

Hence, the compound interest for the second year = ₹ 660 and the sum due at the end of third year = ₹ 7,986.

Calculate the amount and the compound interest on ₹5,000 in 2 years when the rate of interest for successive years is 6% and 8% respectively.

Answer

Given:

Principal (P) = ₹ 5,000

Rate of interest for the first year = 6% p.a.

Rate of interest for the second year = 8% p.a.

Principal for the first year = ₹ 5,000

$\Rightarrow \text{Interest for the first year} = ₹ \dfrac{5000 \times 6 \times 1}{100} = ₹ 300$

Amount at the end of first year = ₹ 5,000 + ₹ 300 = ₹ 5,300

Principal for the second year = ₹ 5,300

$\Rightarrow \text{Interest for the second year} = ₹ \dfrac{5300 \times 8 \times 1}{100} = ₹ 424$

Amount at the end of second year = ₹ 5,300 + ₹ 424 = ₹ 5,724

Compound interest = Final amount - Original principal

= ₹ 5,724 - ₹ 5,000

= ₹ 724

Hence, the amount = ₹ 5,724 and the compound interest = ₹ 724.

Calculate the difference between the compound interest and the simple interest on ₹20,000 in 2 years at 8% per annum.

Answer

Given:

Principal (P) = ₹ 20,000

Rate of interest (R) = 8% p.a.

Time (T) = 2 years

Simple interest :

As we know:

$\text{S.I.} = \dfrac{\text{P} \times \text{R} \times \text{T}}{100}$

Substituting the values, we get

$\Rightarrow \text{S.I.} = ₹ \dfrac{20000 \times 8 \times 2}{100} \\[1em] \Rightarrow \text{S.I.} = ₹ \dfrac{320000}{100} \\[1em] \Rightarrow \text{S.I.} = ₹ 3{,}200$

Compound interest :

Principal for the first year = ₹ 20,000

$\Rightarrow \text{Interest for the first year} = ₹ \dfrac{20000 \times 8 \times 1}{100} = ₹ 1{,}600$

Amount at the end of first year = ₹ 20,000 + ₹ 1,600 = ₹ 21,600

Principal for the second year = ₹ 21,600

$\Rightarrow \text{Interest for the second year} = ₹ \dfrac{21600 \times 8 \times 1}{100} = ₹ 1{,}728$

Compound interest for 2 years = ₹ 1,600 + ₹ 1,728 = ₹ 3,328

Difference between compound interest and simple interest = ₹ 3,328 - ₹ 3,200 = ₹ 128

Hence, the required difference = ₹ 128.