A sum of $1500 is invested at a compound interest rate of 6% per annum. What wil

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Question: A sum of $1500 is invested at a compound interest rate of 6% per annum. What will be the total amount after 3 years?

Options:

Correct Answer: $1890.00

Solution:

Total Amount = P(1 + r/n)^(nt) = 1500(1 + 0.06/1)^(1*3) = 1500(1.191016) = 1786.52.

A sum of $1500 is invested at a compound interest rate of 6% per annum. What will be the total amount after 3 years?

A sum of $1500 is invested at a compound interest rate of 6% per annum. What will be the total amount after 3 years?

Step 1: Identify the principal amount (P), which is $1500.
Step 2: Identify the annual interest rate (r), which is 6% or 0.06 in decimal form.
Step 3: Identify the number of times interest is compounded per year (n), which is 1 for annual compounding.
Step 4: Identify the number of years (t) the money is invested, which is 3 years.
Step 5: Use the compound interest formula: Total Amount = P(1 + r/n)^(nt).
Step 6: Substitute the values into the formula: Total Amount = 1500(1 + 0.06/1)^(1*3).
Step 7: Calculate the expression inside the parentheses: 1 + 0.06 = 1.06.
Step 8: Raise 1.06 to the power of 3: (1.06)^3 = 1.191016.
Step 9: Multiply this result by the principal amount: 1500 * 1.191016 = 1786.52.
Step 10: The total amount after 3 years is $1786.52.

Compound Interest – Understanding how compound interest works, including the formula and its components (principal, rate, time, and compounding frequency).
Mathematical Calculation – Performing calculations accurately, including exponentiation and multiplication.