What is the future value of \$100 compounded annually for 50 years at an annual interest rate of 10\%? (Use the formula: \( FV = PV \times (1 + r)^n \))

• A. \$11,739.09
• B. \$10,000.00
• C. \$1,170.00
• D. \$5,000.00

Answer: (A)

Verified step by step guidance

1. Step 1: Identify the variables in the formula for future value (FV = PV × (1 + r)^n). Here, PV (Present Value) is \$100, r (annual interest rate) is 10% or 0.10, and n (number of years) is 50.
2. Step 2: Convert the annual interest rate from a percentage to a decimal by dividing by 100. For example, 10% becomes 0.10.
3. Step 3: Add 1 to the interest rate (r). This gives (1 + r), which is (1 + 0.10) = 1.10.
4. Step 4: Raise (1 + r) to the power of n (number of years). This means calculating (1.10)^50.
5. Step 5: Multiply the Present Value (PV) by the result from Step 4. This gives FV = 100 × (1.10)^50.