If \$1 is invested today at an annual interest rate of 3.5\% compounded annually, how much will it be worth after 75 years?

• A. \$10.47
• B. \$5.25
• C. \$7.89
• D. \$10.12

Answer: (A)

Verified step by step guidance

1. Understand the concept of compound interest: Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. The formula for compound interest is \( FV = PV \times (1 + r)^n \), where \( FV \) is the future value, \( PV \) is the present value, \( r \) is the annual interest rate, and \( n \) is the number of years.
2. Identify the given values from the problem: \( PV = 1 \), \( r = 0.035 \) (3.5% annual interest rate), and \( n = 75 \) years.
3. Substitute the values into the compound interest formula: \( FV = 1 \times (1 + 0.035)^{75} \). This will calculate the future value of the investment after 75 years.
4. Simplify the expression inside the parentheses: \( 1 + 0.035 = 1.035 \). Then raise \( 1.035 \) to the power of \( 75 \) to account for compounding over 75 years.
5. Multiply the result of \( 1.035^{75} \) by the present value \( PV = 1 \) to find the future value \( FV \). This will give the amount the investment is worth after 75 years.