A loan of $5000 is taken at a compound interest rate of 6% per annum. What will be the total amount to be paid after 3 years? (1910)

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Q: A loan of $5000 is taken at a compound interest rate of 6% per annum. What will be the total amount to be paid after 3 years? (1910)

Solution: Using A = P(1 + r)^t, we find A = 5000(1 + 0.06)^3 = 5000 * 1.191016 = $5955.08, which rounds to $6100.

Steps: 10

Step 1: Identify the principal amount (P), which is the initial loan amount. Here, P = $5000.
Step 2: Identify the annual interest rate (r). Here, r = 6%, which can be written as a decimal: 0.06.
Step 3: Identify the time period (t) in years. Here, t = 3 years.
Step 4: Use the compound interest formula A = P(1 + r)^t to calculate the total amount (A).
Step 5: Substitute the values into the formula: A = 5000(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 this result by the principal amount: A = 5000 * 1.191016.
Step 9: Calculate the total amount: A = 5955.08.
Step 10: Round the total amount to the nearest dollar if necessary. Here, it rounds to $5955.