A sum of money amounts to Rs. 10240 in 2 years at 6 % per annum, compounded annually. Find the sum.

Question

Philoid · Accepted Answer

Let sum = P

Interest rate = 6% = (20/3) % per annum

Time = 2 years

Now,

Amount (A) = P (1 + R/100)ⁿ [Where, P = Present value

R = Annual interest rate

n = Time in years]

∴ A = P[1 + (20/3)/100]²

⇒ 10240 = P [1 + 1/15]²

⇒ 10240 = P [16/15]²

⇒ 10240 = P × 256/225

⇒ P = 10240 × 225/256

⇒ P = 40 × 225

⇒ P = 9000

∴ Sum = Rs.9000