Anand borrowed a certain sum from Anil at a certain rate of simple int

1.	Anand borrowed a certain sum from Anil at a certain rate of simple interest for 2 years. He lent this sum to Shyam at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 630 as compound interest but paid Rs. 600 only as simple interest. Find the rate of interest1). 15%2). 20%3). 35%4). 10%
Answer» Now the formula for simple interest can be given as SI = P × R × T/100 Where SI = Simple Interest, P = PRINCIPAL, R = Rate of interest, T = Time period ∴ 600 = P × R × 2/100 ∴ P × R = 30000-------- equation 1 Now the formula for compound interest can be given as CI = P(1 + R/100)^t - P Where CI = Compound Interest ∴ 630 = P(1 + R/100)² - P-----------equation 2 Put the value of P from equation 1 in equation 2 ∴ 630 = 30000/R(1 + R/100)² - 30000/R ∴ 630 = 30000/R(1 + 2R/100 + R²/10000) - 30000/R (Using the formula (a + b)² = a² + 2ab + b²) ∴ 630 = 30000/R + 600 + 3R - 30000/R ∴ 630 = 600 + 3R ∴ 3R = 30 ∴ R = 10

Anand borrowed a certain sum from Anil at a certain rate of simple interest for 2 years. He lent this sum to Shyam at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 630 as compound interest but paid Rs. 600 only as simple interest. Find the rate of interest1). 15%2). 20%3). 35%4). 10%

Answer»

Now the formula for simple interest can be given as

SI = P × R × T/100

Where SI = Simple Interest, P = PRINCIPAL, R = Rate of interest, T = Time period

∴ 600 = P × R × 2/100

∴ P × R = 30000-------- equation 1

Now the formula for compound interest can be given as

CI = P(1 + R/100)^t - P

Where CI = Compound Interest

∴ 630 = P(1 + R/100)² - P-----------equation 2

Put the value of P from equation 1 in equation 2

∴ 630 = 30000/R(1 + R/100)² - 30000/R

∴ 630 = 30000/R(1 + 2R/100 + R²/10000) - 30000/R (Using the formula (a + b)² = a² + 2ab + b²)

∴ 630 = 30000/R + 600 + 3R - 30000/R

∴ 630 = 600 + 3R

∴ 3R = 30

∴ R = 10