If $2000 is invested at a compound interest rate of 6% per annum, what will be t

₹0.0

Question: If $2000 is invested at a compound interest rate of 6% per annum, what will be the total amount after 5 years?

Options:

Correct Answer: $2676.00

Solution:

Total Amount = 2000(1 + 0.06)^5 = 2000(1.338225) = 2676.45, rounded to $2676.00

If $2000 is invested at a compound interest rate of 6% per annum, what will be the total amount after 5 years?

If $2000 is invested at a compound interest rate of 6% per annum, what will be the total amount after 5 years?

Step 1: Identify the principal amount (initial investment), which is $2000.
Step 2: Identify the annual interest rate, which is 6%. Convert this percentage to a decimal by dividing by 100: 6% = 0.06.
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 = 2000 × (1 + 0.06)^5.
Step 6: Calculate (1 + 0.06) = 1.06.
Step 7: Raise 1.06 to the power of 5: (1.06)^5 = 1.338225.
Step 8: Multiply the principal amount by this result: Total Amount = 2000 × 1.338225.
Step 9: Calculate the final amount: Total Amount = 2676.45.
Step 10: Round the final amount to the nearest cent: $2676.45 rounds to $2676.00.

Compound Interest – Understanding how compound interest works, including the formula for calculating the total amount after a certain number of years.
Exponents – Applying exponentiation in the context of compound interest to determine the growth factor over multiple periods.
Rounding – Knowing how to round the final amount to the nearest cent or dollar as required.