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Here is the problem: Compound interest: 1000 at 5 percent compounded annually for 2 years. What is the amount?

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Principal 1000, annual rate 5 percent, compounded annually, time 2 years; the final amount is unknown. Compound interest, compounded annually; P equals 1000, r equals 5 percent, t equals 2; solve for A.

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Read the problem. Principal 1000, annual rate 5 percent, compounded annually, time 2 years; the final amount is unknown.

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Identify the known values. Compound interest. Known: P equals 1000, r equals 5 percent, t equals 2. Unknown: final amount (A).

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Write the equation. A equals P(1 plus r/1) to the power 1 times t), r as a decimal (compounded annually).

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Solve for A. A equals 1000 times (1 plus 0.05 over 1) to the power 1 times 2).

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Continue. Growth factor equals 1.1025.

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Result. A equals 1102.5.

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So the answer is Final amount equals 1102.5; interest earned equals 102.5.

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Substitute the known values into A equals P(1 plus r/1) to the power 1 times t), r as a decimal and isolate A. Keep units consistent (for example miles, miles per hour and hours).

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Substituting A equals 1102.5 back into A equals P(1 plus r/1) to the power 1 times t), r as a decimal balances both sides, which checks out.