Quantity B: A man borrowed a sum of Rs. 25000 from bank at 10% interes

1.	Quantity B: A man borrowed a sum of Rs. 25000 from bank at 10% interest per annum. He pays back Rs. 10000 at the end of each year. Calculate how much amount he will have to pay at the end of 3rd year to clear his dues? 1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B
Answer» Quantity A: Price of mobile = Rs. 26040 and rate of interest = 12.5% = 1/8 Let the amount of each installment is Rs. x and principals for three years are P₁, P₂ and P₃. First year: x = P₁(1 + 1/8) ⇒ P₁ = 8x/9 Second year: x = P₂(1 + 1/8)² ⇒ P₂ = 64x/81 Third year: x = P₃(1 + 1/8)³ ⇒ P₃ = 512x/729 Sum of principle for 3 years = 26040. ∴ 8x/9 + 64x/81 + 512x/729 = 26040 ⇒ 1736x/729 = 26040 ⇒ x = 15 × 729 ⇒ x = Rs. 10935 ∴ Amount of each installment = Rs. 10935 Quantity B: Man borrowed a sum of Rs. 25000 from BANK at 10% interest PER annum. ∴ Amount after 1 year = 25000 × 1.1 = Rs. 27500 Since he pays Rs. 10000 at the end of each year. ∴ Principal for second year = 27500 – 10000 = Rs. 17500 ∴ Amount after 2 year = 17500 × 1.1 = Rs. 19250 Principal for third year = 19250 – 10000 = Rs. 9250 ∴ Amount after 3 year = 9250 × 1.1 = Rs. 10175 ∴ He will have to pay Rs. 10175 at the end of 3^rd year to clear his dues. ∴ Quantity A > Quantity B

Quantity B: A man borrowed a sum of Rs. 25000 from bank at 10% interest per annum. He pays back Rs. 10000 at the end of each year. Calculate how much amount he will have to pay at the end of 3rd year to clear his dues? 1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B

Answer»

Quantity A:

Price of mobile = Rs. 26040 and rate of interest = 12.5% = 1/8

Let the amount of each installment is Rs. x and principals for three years are P₁, P₂ and P₃.

First year:

x = P₁(1 + 1/8)

⇒ P₁ = 8x/9

Second year:

x = P₂(1 + 1/8)²

⇒ P₂ = 64x/81

Third year:

x = P₃(1 + 1/8)³

⇒ P₃ = 512x/729

Sum of principle for 3 years = 26040.

∴ 8x/9 + 64x/81 + 512x/729 = 26040

⇒ 1736x/729 = 26040

⇒ x = 15 × 729

⇒ x = Rs. 10935

∴ Amount of each installment = Rs. 10935

Quantity B:

Man borrowed a sum of Rs. 25000 from BANK at 10% interest PER annum.

∴ Amount after 1 year = 25000 × 1.1 = Rs. 27500

Since he pays Rs. 10000 at the end of each year.

∴ Principal for second year = 27500 – 10000 = Rs. 17500

∴ Amount after 2 year = 17500 × 1.1 = Rs. 19250

Principal for third year = 19250 – 10000 = Rs. 9250

∴ Amount after 3 year = 9250 × 1.1 = Rs. 10175

∴ He will have to pay Rs. 10175 at the end of 3^rd year to clear his dues.

∴ Quantity A > Quantity B