Simple Interest and Compound Interest — Exercise 8(D)

Find the amount and the compound interest on ₹ 1,20,000 at 8% per annum for 1 year, compounded half-yearly.

Answer

Here,

P = ₹ 1,20,000, R = 8% per annum = 4% per half year

and n = 1 year = 2 half years.

$\text{Amount after 1 year} = 120000 \times \left(1 + \dfrac{4}{100}\right)^2\\[1em] = 120000 \times \dfrac{26}{25} \times \dfrac{26}{25}\\[1em] = 129792$

∴ C.I. = (Amount) − (Principal) = ₹ (1,29,792 − 1,20,000) = ₹ 9,792

Hence, amount = ₹ 1,29,792 and compound interest = ₹ 9,792.

Find the amount and the compound interest on ₹ 32,500 for 1 year; at 12% per annum, compounded half yearly.

Answer

Here,

P = ₹ 32,500, R = 12% per annum = 6% per half year

and n = 1 year = 2 half years.

$\text{Amount after 1 year} = 32500 \times \left(1 + \dfrac{6}{100}\right)^2\\[1em] = 32500 \times \dfrac{53}{50} \times \dfrac{53}{50}\\[1em] = 36517$

∴ C.I. = (Amount) − (Principal) = ₹ (36,517 − 32,500) = ₹ 4,017

Hence, amount = ₹ 36,517 and compound interest = ₹ 4,017.

Calculate the amount and the compound interest on ₹ 24,000 for $1\dfrac{1}{2}$ years at 10% per annum, compounded half-yearly.

Answer

Here,

P = ₹ 24,000, R = 10% per annum = 5% per half year

and n = $1\dfrac{1}{2}$ years = 3 half years.

$\text{Amount after } 1\dfrac{1}{2} \text{ years} = 24000 \times \left(1 + \dfrac{5}{100}\right)^3\\[1em] = 24000 \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20}\\[1em] = 27783$

∴ C.I. = (Amount) − (Principal) = ₹ (27,783 − 24,000) = ₹ 3,783

Hence, amount = ₹ 27,783 and compound interest = ₹ 3,783.

Calculate the amount and the compound interest on ₹ 10,000 for 6 months at 12% per annum, compounded quarterly.

Answer

Here,

P = ₹ 10,000, R = $\dfrac{12}{4}$% per quarter = 3% per quarter

and n = 6 months = 2 quarters.

$\text{Amount after 6 months} = 10000 \times \left(1 + \dfrac{3}{100}\right)^2\\[1em] = 10000 \times \dfrac{103}{100} \times \dfrac{103}{100}\\[1em] = 10609$

∴ C.I. = (Amount) − (Principal) = ₹ (10,609 − 10,000) = ₹ 609

Hence, amount = ₹ 10,609 and compound interest = ₹ 609.

Calculate the amount and the compound interest on ₹ 15,625 for 9 months at 16% per annum, compounded quarterly.

Answer

Here,

P = ₹ 15,625, R = $\dfrac{16}{4}$% per quarter = 4% per quarter

and n = 9 months = 3 quarters.

$\text{Amount after 9 months} = 15625 \times \left(1 + \dfrac{4}{100}\right)^3\\[1em] = 15625 \times \dfrac{26}{25} \times \dfrac{26}{25} \times \dfrac{26}{25}\\[1em] = 17576$

∴ C.I. = (Amount) − (Principal) = ₹ (17,576 − 15,625) = ₹ 1,951

Hence, amount = ₹ 17,576 and compound interest = ₹ 1,951.

Calculate the amount and the compound interest on ₹ 25,60,000 for 1 year at 10% per annum, compounded quarterly.

Answer

Here,

P = ₹ 25,60,000, R = $\dfrac{10}{4}$% per quarter = $\dfrac{5}{2}$% per quarter

and n = 1 year = 4 quarters.

$\text{Amount after 1 year} = 2560000 \times \left(1 + \dfrac{5}{2 \times 100}\right)^4\\[1em] = 2560000 \times \dfrac{41}{40} \times \dfrac{41}{40} \times \dfrac{41}{40} \times \dfrac{41}{40}\\[1em] = 2825761$

∴ C.I. = (Amount) − (Principal) = ₹ (28,25,761 − 25,60,000) = ₹ 2,65,761

Hence, amount = ₹ 28,25,761 and compound interest = ₹ 2,65,761.