- The problem demonstrates the calculation of future value (FV) for a lump sum investment using compound interest.
- An initial principal (PV) of $100 is invested at an annual interest rate (r) of 10% (or 0.10).
- The future value after t years is calculated using the formula: FVₜ = PV × (1 + r)ᵗ.
- Year 1: FV₁ = $100 × (1 + 0.10)¹ = $110.00. Interest earned is $10.00.
- Year 2: FV₂ = $100 × (1 + 0.10)² = $121.00. Interest earned is $11.00 (calculated on the new balance of $110).
- Year 3: FV₃ = $100 × (1 + 0.10)³ = $133.10. Interest earned is $12.10 (calculated on the new balance of $121).
- This process continues, with interest earned each year being calculated on the previous year's ending amount, demonstrating compounding.
- The table extends this calculation through Year 5, showing the beginning amount, interest earned, and ending amount for each year.
- By Year 5, the ending amount is $161.05. The total interest earned over the 5 years is the sum of the yearly interest amounts, which equals $61.05.
- The expression (1 + r)ᵗ is defined as the future value interest factor, which, when multiplied by the present value, gives the future value.
- Calculator setup instructions are provided for BA II Plus (set decimal places to 9) and note that TI-83/84 calculators do not require this initial setup.
Parent Tip: Review the logic above to help your child master the concept of time and money worksheet for.
