Final answer:
To calculate how much Oriole Productions borrowed, we use the present value of an annuity due formula, considering the annual payment of $1,512,000, the interest rate of 18.40%, and a term of seven years.
Step-by-step explanation:
Oriole Productions needs to determine the amount borrowed from the California Finance Company by calculating the present value of an annuity. Since payments are made annually at the beginning of each period, we are dealing with an annuity due situation. The formula for the present value of an annuity due takes into account the payment amount, the interest rate, and the number of periods. By applying this formula and using the information provided, we can find out the loan amount Oriole Productions borrowed.
The formula for the present value of an annuity due is as follows:
PV_\text{annuity due} = R \times \left(\frac{1 - (1+r)^{-n}}{r}\right) \times (1 + r)
Where:
- PV_\text{annuity due} is the present value of the annuity due
- R is the regular payment amount
- r is the interest rate per period
- n is the total number of periods
By plugging in the values: R = $1,512,000, r = 18.40% (or 0.1840 as a decimal), and n = 7 years, we can calculate the present value of the loan.
However, without a financial calculator or spreadsheet software, it is complex to compute this manually due to the nature of the formula.