True discount on a short-term bill at simple interest Find the true discount on a bill of $1,260 due in 6 months at 10% per annum (simple interest).

Introduction / Context:
True discount is the difference between the amount due (the bill amount) and its present worth when discounted at a given simple interest rate for the time until maturity. It represents the exact rebate for early payment.

Given Data / Assumptions:

• S (amount due) = $1,260.
• Time to maturity t = 6 months = 0.5 year.
• Simple interest rate r = 10% per annum.

Concept / Approach:
Present worth PW = S / (1 + r * t). True discount TD = S − PW. Under simple interest, this is the precise rebate to make parties indifferent between paying now and paying at maturity.

Step-by-Step Solution:
r * t = 0.10 * 0.5 = 0.05.PW = 1,260 / 1.05 = $1,200.TD = 1,260 − 1,200 = $60.

Verification / Alternative check:
If $1,200 were invested at 10% for 6 months, it would grow to 1,200 * 1.05 = $1,260, matching the bill amount. Hence $60 is the correct true discount.

Why Other Options Are Wrong:
$160 and $260 are far too large; $80 overstates the rebate; $63 is an off-by-error not supported by the formula.

Common Pitfalls:
Computing bank discount (on the amount) instead of true discount, or forgetting to use present worth first. Carefully apply PW = S / (1 + r * t).

Final Answer:
$ 60