Initial value, P = Rs.65536

Interest rate, R = (25/2)% per annum

Time, n = 2 years

∵ Compounded annually.

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

R = Annual interest rate

n = Time in years]

∴ A = 65536 [1 +(25/2) /100]²

⇒ A = 65536 [1 + 1/8]²

⇒ A = 65536 [9/8]²

⇒ A = 65536 × 9/8 × 9/8

⇒ A = 65536 × 81/64

⇒ A = 1024 × 81

⇒ A = 82944

∴ Amount = Rs.82944

∴ Compound interest = Rs.(82944 – 65536) [∵CI = A – P]

= Rs.17408

Now,

∵ Compounded half-yearly.

∴ Amount (A) = P [1 + (R/2)/100]²ⁿ [Where, P = Present value

R = Annual interest rate

n = Time in years]

∴ A = 65536 [1 + (25/4)/100]⁴ [R = (25/2)% and n = 2 years]

⇒ A = 65536 [1 + 1/16]⁴

⇒ A = 65536 [17/16]⁴

⇒ A = 65536 × 17/16 × 17/16 × 17/16 × 17/16

⇒ A = 65536 × 83521/65536

⇒ A = 1 × 83521

⇒ A = 83521

∴ Amount = Rs.83521

∴ Compound interest = Rs.(83521 – 65536) [∵CI = A – P]

= Rs.17985

Now,

Difference between interests compound half-yearly and yearly,

= Rs.(17985 – 17408)

= Rs.577