A sum of money was lent for 2 years at 20% compounded annually. If the

1.	A sum of money was lent for 2 years at 20% compounded annually. If the interest is payable half-yearly instead of yearly, then the interest is Rs. 482 more. Find the sum.
Answer» Given details are, Rate (r) = 20% per annum = 20/2 = 10% (half yearly) Time (t) = 2 years = 2 × 2 = 4 half years Principal be = Rs P P (1 + R/100)ⁿ – P (1 + R/100)ⁿ = 482 P (1 + 10/100)⁴ – P (1 + 20/100)² = 482 P (110/100)⁴ – P (120/100)² = 482 P (1.4641) – P (1.44) = 482 0.0241P = 482 P = 482/0.0241 = 20000 ∴ Amount is Rs 20000.

A sum of money was lent for 2 years at 20% compounded annually. If the interest is payable half-yearly instead of yearly, then the interest is Rs. 482 more. Find the sum.

Answer»

Given details are,

Rate (r) = 20% per annum = 20/2 = 10% (half yearly)

Time (t) = 2 years = 2 × 2 = 4 half years

Principal be = Rs P

P (1 + R/100)ⁿ – P (1 + R/100)ⁿ = 482

P (1 + 10/100)⁴ – P (1 + 20/100)² = 482

P (110/100)⁴ – P (120/100)² = 482

P (1.4641) – P (1.44) = 482

0.0241P = 482

P = 482/0.0241

= 20000

∴ Amount is Rs 20000.