Final answer:
To calculate the future value of Builder Products Incorporated's ordinary annuity of $6,000 per year at 12% interest rate for four years, we use the future value formula for annuities, considering each payment compounded at the interest rate until the end of the fourth year.
Step-by-step explanation:
To calculate the future value of an ordinary annuity, we use the future value formula for annuities. For Builder Products Incorporated, receiving $6,000 per year at an interest rate of 12% for four years, the future value is calculated by summing up the value of each annuity payment compounded at the interest rate until the end of the fourth year.
The future value (FV) formula for an ordinary annuity is expressed as:
FV = C × ((1 + r)n - 1) / r
Where:
- C is the cash flow per period ($6,000)
- r is the interest rate (12% or 0.12)
- n is the number of periods (4)
The calculation steps are as follows:
- Convert the interest rate from a percentage to a decimal: 12% = 0.12.
- Calculate the factor (1 + r)n: (1 + 0.12)4.
- Compute the total factor for the annuity: ((1 + 0.12)4 - 1) / 0.12.
- Multiply this factor by the cash flow per period: $6,000 × total factor.
- This calculation gives you the future value of the annuity after four years.
Using this formula, the future value of the annuity can be calculated step-by-step to determine the amount Builder Products Incorporated will receive in year four.