If a sum of money amounts to $8000 in 3 years at compound interest, what was the principal if the rate of interest is 5%?

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Q: If a sum of money amounts to $8000 in 3 years at compound interest, what was the principal if the rate of interest is 5%?

Solution: Let P be the principal. A = P(1 + r)^n; 8000 = P(1 + 0.05)^3; P = 8000 / 1.157625 = $6912.87.

Steps: 9

Step 1: Identify the total amount after 3 years, which is $8000.
Step 2: Identify the rate of interest, which is 5% or 0.05 in decimal form.
Step 3: Identify the number of years, which is 3.
Step 4: Use the formula for compound interest: A = P(1 + r)^n, where A is the amount, P is the principal, r is the rate, and n is the number of years.
Step 5: Substitute the known values into the formula: 8000 = P(1 + 0.05)^3.
Step 6: Calculate (1 + 0.05)^3, which equals 1.157625.
Step 7: Rewrite the equation: 8000 = P * 1.157625.
Step 8: Solve for P by dividing both sides by 1.157625: P = 8000 / 1.157625.
Step 9: Calculate the value of P, which is approximately $6912.87.