Abhay borrowed ₹ 16000 at 7 ½ % per annum simple interest. On the s

1.	Abhay borrowed ₹ 16000 at 7 ½ % per annum simple interest. On the same day, he lent it to gurmeet at the same rate but compounded annually. What does he gain at the end of 2 years?
Answer» Given: Present value= ₹ 16000 Interest rate= 7 ½ % per annum= 15/2 % Time=2 years Now find compound interest, To find the amount we have the formula, Amount (A) = P (1+(R/100))ⁿ Where P is present value, r is rate of interest, n is time in years. Now substituting the values in above formula we get, ∴ A = 16000 (1 + (15/2)/100)² ⇒ A = 16000 (1+3/40)² ⇒ A =16000 (43/40)² ⇒ A = 16000 (1894/1600) ⇒ A = ₹ 18490 ∴ Compound interest = A – P = 18490 – 16000 = ₹ 2490 Now find the simple interest, Simple interest (SI) = PTR/100 Where P is principle amount, T is time taken, R is rate per annum SI = (16000 × (15/2) × 2) / 100 = 160 × 15 = ₹ 2400 Abhay gains at the end of 2 year= (CI – SI) = 2490 – 2400 = ₹ 90

Abhay borrowed ₹ 16000 at 7 ½ % per annum simple interest. On the same day, he lent it to gurmeet at the same rate but compounded annually. What does he gain at the end of 2 years?

Answer»

Given:

Present value= ₹ 16000

Interest rate= 7 ½ % per annum= 15/2 %

Time=2 years

Now find compound interest,

To find the amount we have the formula,

Amount (A) = P (1+(R/100))ⁿ

Where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴ A = 16000 (1 + (15/2)/100)²

⇒ A = 16000 (1+3/40)²

⇒ A =16000 (43/40)²

⇒ A = 16000 (1894/1600)

⇒ A = ₹ 18490

∴ Compound interest = A – P

= 18490 – 16000 = ₹ 2490

Now find the simple interest,

Simple interest (SI) = PTR/100

Where P is principle amount, T is time taken, R is rate per annum

SI = (16000 × (15/2) × 2) / 100

= 160 × 15

= ₹ 2400

Abhay gains at the end of 2 year= (CI – SI)

= 2490 – 2400

= ₹ 90