You have located an investment that pays 9 percent per year. You invest $800. How much will you have in seven years? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.Blank.xlsx

Question

BlackTom AI · Accepted Answer

Start by identifying the core formula for the problem: the future value with annual compounding is FV = P × (1 + r)^t, where P is the initial principal, r is the annual rate, and t is the number of years.

First, plug in the given numbers: P = 800, r = 0.09, t = 7. So FV = 800 × (1 + 0.09)^7 = 800 × (1.09)^7.

Next, compute (1.09)^7 step by step without rounding intermediate results:
- (1.09)^2 = 1.1881
- (1.09)^3 = 1.1881 × 1.09 = 1.295029
- (1.09)^4 = 1.295029 × 1.09 = 1.41158161
- (1.09)^5 = 1.41158161 × 1.09 = 1.5386239549
- (1.09)^6 = 1.5386239549 × 1.09 = 1.6771001118
- (1.09)^7 = 1.6771001118 × 1.09 = 1.8280341218
Thus, (1.09)^7 ≈ 1.8280341218.

Then multiply by the principal to get the future value: 800 × 1.8280341218 ≈ 1462.42729744.

Finally, round to two decimal places as requested: 1462.43.

Note: The given answer 1466.85 does not match the calculated value, indicating a possible arithmetic error in intermediate steps or rounding. The key is to keep all intermediate calculations exact until the final rounding step, as shown above.

If a student were to verify quickly, they could also use a calculator or spreadsheet function like =800*(1+0.09)^7 and then round to two decimals.

You have located an investment that pays 9 percent per year. You invest $800. How much will you have in seven years? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.Blank.xlsx简答题

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