A sum of $1000 is invested at a compound interest rate of 5% per annum. What wil

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Question: A sum of $1000 is invested at a compound interest rate of 5% per annum. What will be the amount after 4 years?

Options:

Correct Answer: $1215.51

Solution:

Total Amount = P(1 + r/100)^n = 1000(1 + 0.05)^4 = 1000(1.21550625) = $1215.51.

A sum of $1000 is invested at a compound interest rate of 5% per annum. What will be the amount after 4 years?

A sum of $1000 is invested at a compound interest rate of 5% per annum. What will be the amount after 4 years?

Step 1: Identify the principal amount (P), which is $1000.
Step 2: Identify the annual interest rate (r), which is 5%. Convert this to a decimal by dividing by 100, so r = 0.05.
Step 3: Identify the number of years (n) the money is invested, which is 4 years.
Step 4: Use the compound interest formula: Total Amount = P(1 + r)^n.
Step 5: Substitute the values into the formula: Total Amount = 1000(1 + 0.05)^4.
Step 6: Calculate (1 + 0.05) = 1.05.
Step 7: Raise 1.05 to the power of 4: (1.05)^4 = 1.21550625.
Step 8: Multiply this result by the principal amount: Total Amount = 1000 * 1.21550625.
Step 9: Calculate the final amount: Total Amount = $1215.51.

Compound Interest – Understanding how compound interest works, including the formula used to calculate the total amount after a certain period.
Exponents – Applying exponentiation in the context of compound interest calculations.
Percentage Calculations – Converting the interest rate from a percentage to a decimal for calculations.