On 1 September 2019, Cindy's Jewellery deposited $10 000 in a Term Deposit at a fixed rate of 12%. Interest on the Term Deposit is only paid once per year on 1 January. On balance day (30 September 2019) identify the amount of accrued revenue Cindy's Jewellery had earned on the Term Deposit.

Question

BlackTom AI · Accepted Answer

We start by restating the scenario to ensure we’re applying the right timing.
- The term deposit is $10,000 at an annual fixed rate of 12%.
- Interest is paid once per year on 1 January, so on balance day 30 September 2019 we need the accrued interest from Sep 1 to Sep 30, 2019, which is 30 days of the year.

Now evaluate each option:
Option a: $100
- This represents 12% annual interest pro-rated for 30 days using a 360-day year, since 10,000 × 12% × (30/360) = 10,000 × 0.12 × 0.0833... = 100.
- If the problem assumes a 360-day year for simplicity (common in accounting problems), this is a clean and conventional calculation.

Option b: $400
- This would correspond to 10,000 × 12% × (30/225) or similar, which does not align with standard year-day conventions for pro-rating interest. It overstates the accrual for 30 days.
- It implies a much shorter denominator or a misapplication of the rate, not consistent with typical practice.

Option c: $120
- This equals 10,000 × 12% × (30/300) if you were using a 300-day year, which is not standard. It also would imply 3% of the principal for 30 days, which conflicts with the 12% annual rate.
- The calculation here misaligns with the given annual rate and standard day-count conventions.

Option d: $1,200
- This is the full-year interest on $10,000 at 12% (10,000 × 12% = 1,200). Since only 30 days out of 360 or 365 days have elapsed, this would overstate accrual by a factor of about 12.
- It represents annual interest, not the accrued portion for the short window provided.

To determine the correct accrued revenue, we must apply the annual rate to the proportion of the year that has elapsed (30 days out of the year). Using a conventional approach:
- If a 360-day year is used: accrued interest = 10,000 × 0.12 × (30/360) = 100.
- If a 365-day year is used: accrued interest ≈ 10,000 × 0.12 × (30/365) ≈ 98.6, which would typically be rounded to 100 in many accounting contexts.

Therefore, among the given options, the one that aligns with common accounting practice for pro-rating annual interest over 30 days is $100, which matches option a. The other options involve overestimation (1000+), incorrect day-count conventions, or full-year interest, none of which correctly reflect the accrued revenue for a 30-day period after the deposit date.

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