In how many years will Rs. 1800 amount to Rs. 2178 at 10% per annum wh

1.	In how many years will Rs. 1800 amount to Rs. 2178 at 10% per annum when compounded annually?
Answer» Let time = n years P = Rs.1800 A = Rs.2178 R = 10% per annum Now, Amount (A) = P (1 + R/100)ⁿ [Where, A = Amount with compound interest P = Present value R = Annual interest rate n = Time in years] ∴ A = P (1 + R/100)ⁿ ⇒ 2178 = 1800 (1 + 10/100)ⁿ ⇒ (1 + 1/10)ⁿ= 2178/1800 ⇒ (11/10)ⁿ = 121/100 ⇒ (11/10)ⁿ = (11/10)² ⇒ n = 2 ∴ Time = 2 years.

In how many years will Rs. 1800 amount to Rs. 2178 at 10% per annum when compounded annually?

Answer»

Let time = n years

P = Rs.1800

A = Rs.2178

R = 10% per annum

Now,

Amount (A) = P (1 + R/100)ⁿ [Where, A = Amount with compound interest

P = Present value

R = Annual interest rate

n = Time in years]

∴ A = P (1 + R/100)ⁿ

⇒ 2178 = 1800 (1 + 10/100)ⁿ

⇒ (1 + 1/10)ⁿ= 2178/1800

⇒ (11/10)ⁿ = 121/100

⇒ (11/10)ⁿ = (11/10)²

⇒ n = 2

∴ Time = 2 years.