Question

Find the compound interest on Rs. 20,000 in 2 years at 4 % per annum, the interest being compounded half-yearly.

Answer 1

CI = Principal (1 + r/100)^t - Principal

Its calculated half yearly so rate will get half and time will get doubled

= 20000 (1 + 2/100)^4 - 20000

= 20000 (51/50)^4 - 20000

= 20000 * 51/50 * 51/50 * 51/50 * 51/50 - 20000

= 21648.64 - 20000

= 1648.64

Answer 2

SOLUTION :  

Given :

Principal(P) = ₹ 20000

Time(n) = 2 years

Rate(R) = 4%

FOR HALF YEARLY : Rate gets half(R/2) and time gets doubled(2n)

Time(n) = 2 ×2 = 4 years

Rate(R) = 4 /2 = 2%

A = P(1 + R/100)ⁿ

A= 20000 (1 + 2/100)⁴

A= 20000 (1 + 1/50)⁴

A= 20000 (51/50)⁴

A= 20000 × 51/50 × 51/50 × 51/50 × 51/50

A = 2 × 51 ×51×51×51/ 5×5×5×5

A=  13,530,402/ 625

A= ₹ 21,648.64

C.I = Amount (A) - principal(P)  

Compound Interest (C.I) = 21648.64 - 20000

C.I = ₹ 1648.64

Hence, the compound interest is ₹ 1648.64

HOPE THIS ANSWER WILL HELP YOU...