If a sum of money is invested at a compound interest rate of 6% per annum, how much will it grow in 5 years?

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Q: If a sum of money is invested at a compound interest rate of 6% per annum, how much will it grow in 5 years?

Solution: Using A = P(1 + r)^t, A = 1000(1 + 0.06)^5 = 1000 * 1.338225 = 1338.23.

Steps: 9

Step 1: Identify the formula for compound interest, which is A = P(1 + r)^t.
Step 2: Determine the values needed for the formula: P (the principal amount), r (the interest rate), and t (the time in years).
Step 3: In this case, let's assume P = 1000 (the initial amount), r = 0.06 (6% as a decimal), and t = 5 (years).
Step 4: Substitute the values into the formula: A = 1000(1 + 0.06)^5.
Step 5: Calculate (1 + 0.06) which equals 1.06.
Step 6: Raise 1.06 to the power of 5: 1.06^5 = 1.338225.
Step 7: Multiply this result by the principal amount: A = 1000 * 1.338225.
Step 8: Calculate the final amount: A = 1338.225.
Step 9: Round the final amount to two decimal places: A = 1338.23.