A sum of money invested at compound interest grows to $5000 in 4 years at a rate of 6% per annum. What was the principal?

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Q: A sum of money invested at compound interest grows to $5000 in 4 years at a rate of 6% per annum. What was the principal?

Solution: Let P be the principal. A = P(1 + r)^n; 5000 = P(1 + 0.06)^4; P = 5000 / 1.262476 = $3960.00.

Steps: 9

Step 1: Identify the final amount (A), which is $5000.
Step 2: Identify the interest rate (r), which is 6% per annum, or 0.06 in decimal form.
Step 3: Identify the number of years (n), which is 4 years.
Step 4: Write the formula for compound interest: A = P(1 + r)^n.
Step 5: Substitute the known values into the formula: 5000 = P(1 + 0.06)^4.
Step 6: Calculate (1 + 0.06)^4, which equals approximately 1.262476.
Step 7: Rewrite the equation: 5000 = P * 1.262476.
Step 8: Solve for P by dividing both sides by 1.262476: P = 5000 / 1.262476.
Step 9: Calculate the value of P, which is approximately $3960.00.