Answer:
![P=\$24,828.73](https://tex.z-dn.net/?f=P%3D%5C%2424%2C828.73)
Step-by-step explanation:
<u>Future Value of Annuities</u>
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
![\displaystyle PV=P\cdot \frac{1-(1+i)^{-n}}{i}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20PV%3DP%5Ccdot%20%5Cfrac%7B1-%281%2Bi%29%5E%7B-n%7D%7D%7Bi%7D)
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
![\displaystyle P=PV\cdot \frac{i}{1-(1+i)^{-n}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%3DPV%5Ccdot%20%5Cfrac%7Bi%7D%7B1-%281%2Bi%29%5E%7B-n%7D%7D)
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
![PV=250,000*(100-20/100)=200,000](https://tex.z-dn.net/?f=PV%3D250%2C000%2A%28100-20%2F100%29%3D200%2C000)
![i=12\%=0.12](https://tex.z-dn.net/?f=i%3D12%5C%25%3D0.12)
![n=30](https://tex.z-dn.net/?f=n%3D30)
Computing P
![\displaystyle P=200,000\cdot \frac{0.12}{1-(1+0.12)^{-30}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%3D200%2C000%5Ccdot%20%5Cfrac%7B0.12%7D%7B1-%281%2B0.12%29%5E%7B-30%7D%7D)
![\boxed{P=\$24,828.73}](https://tex.z-dn.net/?f=%5Cboxed%7BP%3D%5C%2424%2C828.73%7D)