A sum of $3000 is invested at a compound interest rate of 7% per annum. What will be the total amount after 5 years?

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Q: A sum of $3000 is invested at a compound interest rate of 7% per annum. What will be the total amount after 5 years?

Solution: Total Amount = 3000(1 + 0.07)^5 = 3000(1.402552) = 4207.66

Steps: 9

Step 1: Identify the principal amount (the initial investment), which is $3000.
Step 2: Identify the annual interest rate, which is 7%. Convert this percentage to a decimal by dividing by 100. So, 7% becomes 0.07.
Step 3: Identify the number of years the money is invested, which is 5 years.
Step 4: Use the compound interest formula: Total Amount = Principal × (1 + Interest Rate)^(Number of Years).
Step 5: Substitute the values into the formula: Total Amount = 3000 × (1 + 0.07)^5.
Step 6: Calculate (1 + 0.07), which equals 1.07.
Step 7: Raise 1.07 to the power of 5: 1.07^5 = 1.402552.
Step 8: Multiply the principal amount by this result: 3000 × 1.402552 = 4207.66.
Step 9: The total amount after 5 years is $4207.66.