Find the amount and the compound interest on Rs. 31250 for 1
% years at 8% per annum, compounded half-yearly.
Present value, P = Rs.31250
Interest rate, R = 8% per annum
Time, n = (3/2) years
∵ Compounded half-yearly.
∴ Amount (A) = P [1 + (R/2)/100]2n [Where, P = Present value
R = Annual interest rate
n = Time in years]
∴ A = 31250 [1 + (8/2)/100]3 [2n = 2 × 3/2]
⇒ A = 31250 [1 + 4/100]3
⇒ A = 31250 [1 + 1/25]3
⇒ A = 31250 [26/25]3
⇒ A = 31250 × 17576/15625
⇒ A = 2 × 17576
⇒ A = 35152
∴ Amount = Rs.35152
∴ Compound interest = Rs.(35152 – 31250) [∵CI = A – P]
= Rs.3902
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