Answer:
[tex]P=\$24,828.73[/tex]
Step-by-step explanation:
Future Value of Annuities
We can define an annuity as a series of periodic payments that are received at a future date.
The present value of the annuities is the financial sum of them, including the interest paid per period. The equation to compute the present value PV is
[tex]\displaystyle PV=P\cdot \frac{1-(1+i)^{-n}}{i}[/tex]
Where
P is the value of the annual payments
i is the interest rate
n is the number of years to pay the balance
Solving the above equation for P
[tex]\displaystyle P=PV\cdot \frac{i}{1-(1+i)^{-n}}[/tex]
We have the following data
PV is the balance to be paid off, and is the value of the factory minus the 20 percent down as stated in the terms, thus
[tex]PV=250,000*(100-20/100)=200,000[/tex]
[tex]i=12\%=0.12[/tex]
[tex]n=30[/tex]
Computing P
[tex]\displaystyle P=200,000\cdot \frac{0.12}{1-(1+0.12)^{-30}}[/tex]
[tex]\boxed{P=\$24,828.73}[/tex]
