Present worth and true discount at simple interest: Find the present worth (PW) and the true discount (TD) at 6% per annum simple interest for a due amount of $176 payable after 20 months.

Introduction / Context:
True discount is the reduction from the future sum required to obtain its present worth under simple interest. Once the present worth is computed, the true discount is just the difference between the future sum and the present worth.

Given Data / Assumptions:

• Sum due S = $176.
• Time t = 20 months = 20/12 years.
• Rate r = 6% per annum, simple interest.

Concept / Approach:
Under simple interest, Amount = PW * (1 + r t). Therefore PW = S / (1 + r t). True discount TD = S − PW. Using months converted to years keeps the units consistent with an annual rate.

Step-by-Step Solution:

Verification / Alternative check:
Check: PW * (1 + r t) = 160 * 1.10 = 176 equals the sum due, confirming correctness.

Why Other Options Are Wrong:

• Other pairs do not satisfy both PW = S/(1 + r t) and TD = S − PW simultaneously at 6% for 20 months.

Common Pitfalls:
Forgetting to convert months to years or applying the rate twice. Keep the chain: compute r t, then divide S by (1 + r t).

Final Answer:
$ 160, $ 16