A sum of $5000 is invested at a compound interest rate of 6% per annum. What wil

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Question: A sum of $5000 is invested at a compound interest rate of 6% per annum. What will be the amount after 2 years?

Options:

Correct Answer: $5630

Solution:

Amount = P(1 + r/n)^(nt) = 5000(1 + 0.06/1)^(1*2) = 5000(1.1236) = $5630

A sum of $5000 is invested at a compound interest rate of 6% per annum. What will be the amount after 2 years?

A sum of $5000 is invested at a compound interest rate of 6% per annum. What will be the amount after 2 years?

Step 1: Identify the principal amount (P), which is $5000.
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). Since it's compounded annually, n = 1.
Step 4: Identify the number of years the money is invested (t), which is 2 years.
Step 5: Use the compound interest formula: Amount = P(1 + r/n)^(nt).
Step 6: Substitute the values into the formula: Amount = 5000(1 + 0.06/1)^(1*2).
Step 7: Simplify the expression inside the parentheses: 1 + 0.06 = 1.06.
Step 8: Calculate the exponent: 1 * 2 = 2, so we have (1.06)^2.
Step 9: Calculate (1.06)^2, which equals approximately 1.1236.
Step 10: Multiply this result by the principal: Amount = 5000 * 1.1236.
Step 11: Calculate the final amount: 5000 * 1.1236 = $5630.

Compound Interest – The process of earning interest on both the initial principal and the accumulated interest from previous periods.
Formula Application – Understanding and correctly applying the compound interest formula: A = P(1 + r/n)^(nt).
Interest Rate Conversion – Converting the annual interest rate into a decimal for calculations.
Time Period Calculation – Determining the total time the money is invested or borrowed, in years.