A saver in a 360-day year country deposits $500,000 for 120 days at 3.5%pa. How much will the deposit be worth at the completion of the investment?

Question

BlackTom AI · Accepted Answer

First, restate the problem: A saver in a 360-day year country deposits $500,000 for 120 days at 3.5% per annum. How much will the deposit be worth at the completion of the investment?

Option under consideration: $517,500.00.

Step by step analysis of the calculation:
- Determine the interest rate per day using a 360-day year: 3.5% per year means 0.035 per year.
- Convert the investment duration to years using the 360-day year convention: 120 days = 120/360 = 1/3 year.
- Compute the interest earned with simple interest (the common convention in savings for a fixed term in many contexts): Interest = Principal × Rate × Time = 500,000 × 0.035 × (1/3).
- Multiply: 0.035 × (1/3) = 0.011666...; then 500,000 × 0.011666... ≈ 5,833.33.
- Therefore, the accumulated value after 120 days would be: Principal + Interest = 500,000 + 5,833.33 ≈ 505,833.33.

Observation on the provided option:
- The option 517,500.00 corresponds to getting the annual interest of 17,500 (which is 500,000 × 0.035) in total, i.e., assuming the full year (1.0 year) has elapsed rather than 120 days (1/3 year). This would yield 500,000 × (1 + 0.035) = 517,500, which aligns with a 1-year horizon, not 120 days.

Common pitfalls to watch for:
- Mixing up the time fraction: using 120/360 = 1/3 year is correct for 120 days in a 360-day year; using 1 year would overstate the accrued amount for 120 days.
- Confirming whether interest is simple or compounded: for a single fixed-term deposit over a short period like 120 days, simple interest is typically assumed unless stated otherwise; compounding within 120 days would require more frequent compounding details and would usually yield a slightly different result.

In summary, with simple interest, the expected accumulated value after 120 days is approximately $505,833.33, not $517,500.00, given the 360-day year convention and the 120-day term.”

25728 Fixed Income Analysis - Autumn 2025 FIA Quiz 2.1 Short-Term Investment Calculations

A saver in a 360-day year country deposits $500,000 for 120 days at 3.5%pa. How much will the deposit be worth at the completion of the investment?

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