A sum of $1200 is invested at a rate of 6% per annum compounded annually. What w

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Question: A sum of $1200 is invested at a rate of 6% per annum compounded annually. What will be the amount after 3 years?

Options:

Correct Answer: $1449.22

Solution:

Amount = P(1 + r)^n = 1200(1 + 0.06)^3 = 1200(1.191016) = $1430.82.

A sum of $1200 is invested at a rate of 6% per annum compounded annually. What will be the amount after 3 years?

A sum of $1200 is invested at a rate of 6% per annum compounded annually. What will be the amount after 3 years?

Step 1: Identify the principal amount (P), which is $1200.
Step 2: Identify the annual interest rate (r), which is 6%. Convert this to decimal form by dividing by 100: 6% = 0.06.
Step 3: Identify the number of years (n) the money is invested, which is 3 years.
Step 4: Use the formula for compound interest: Amount = P(1 + r)^n.
Step 5: Substitute the values into the formula: Amount = 1200(1 + 0.06)^3.
Step 6: Calculate (1 + 0.06) = 1.06.
Step 7: Raise 1.06 to the power of 3: (1.06)^3 = 1.191016.
Step 8: Multiply the principal amount by this result: Amount = 1200 * 1.191016.
Step 9: Calculate the final amount: Amount = $1430.82.

Compound Interest – Understanding how to calculate the future value of an investment using the formula A = P(1 + r)^n, where A is the amount, P is the principal, r is the interest rate, and n is the number of years.