Find the amount and the compound interest on Rs. 31250 for 1 (1/2)% y

1.	Find the amount and the compound interest on Rs. 31250 for 1 (1/2)% years at 8% per annum, compounded half-yearly.
Answer» 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

Find the amount and the compound interest on Rs. 31250 for 1 (1/2)% years at 8% per annum, compounded half-yearly.

Answer»

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