If the present value is $766.32 and the rate of return is 0.055, how much will you have in one year?

Question

BlackTom AI · Accepted Answer

Restating the problem: The present value is 766.32, the rate of return is 0.055, and we want the amount after one year.
Step 1: Decide the formula. For a single-year horizon with annual compounding, the future value (FV) is FV = PV × (1 + r).
Step 2: Plug in the numbers. FV = 766.32 × (1 + 0.055) = 766.32 × 1.055.
Step 3: Perform the multiplication. 766.32 × 1.055 = 766.32 + (766.32 × 0.055).
Step 4: Compute the interest part: 766.32 × 0.055 = 42.1476.
Step 5: Add the principal: 766.32 + 42.1476 = 808.4676.
Step 6: Round to a reasonable monetary precision. Rounding to the nearest cent yields 808.47.

Assessment of the provided answer: The given figure 806.64 does not match the correct calculation for FV with annual compounding at 5.5% (which is 808.47). This discrepancy could stem from using a different interpretation of the rate (e.g., a different compounding frequency, a misread rate, or a rounding difference before the final step). If the problem had intended simple interest instead of compounding, the calculation would still yield FV = PV × (1 + r × t) = 766.32 × (1 + 0.055 × 1) = 766.32 × 1.055 = 808.4676, which again rounds to 808.47, so the mismatch remains.

Alternative scenarios to consider: If the rate were applied monthly or another compounding schedule, FV would differ (e.g., monthly compounding would make FV > 808.47 but would require a different formula). If someone mistakenly used a rate of 0.0545 or rounded intermediate steps differently, they might arrive at 806.64, but that would be inconsistent with the standard 5.5% annual rate.

Conclusion (based on standard interpretation): The correct future value after one year at 5.5% with annual compounding is 808.47.

FINA2720.MERGED.202610 Practice with Respondus and Time Value of Money- Requires Respondus LockDown Browser

If the present value is $766.32 and the rate of return is 0.055, how much will you have in one year?

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