Answer:
1) payment of  $  78,867.70
2) payment of $ Â 62,614.11
3) 7 years
4) rate of 12%
Explanation:
On the first and second point we need to solve for the PMT:
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV Â $250,000.00
time 4
rate 0.1
[tex]250000 \div \frac{1-(1+0.1)^{-4} }{0.1} = C\\[/tex]
C Â $ 78,867.701
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV Â $250,000.00
time 5
rate 0.08
[tex]250000 \div \frac{1-(1+0.08)^{-5} }{0.08} = C\\[/tex]
C Â $ 62,614.114
In the third one we need to solve for time:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C Â $51,351.00
time n
rate 0.1
PV $250,000.0000
[tex]51351 \times \frac{1-(1+0.1)^{-n} }{0.1} = 250000\\[/tex]
we work to reach this expression:
[tex](1+0.1)^{-n}= 1-\frac{250000\times0.1}{51351}[/tex]
ANd we acn use logarithmics properties to solve for n
[tex]-n= \frac{log0.51315456368912}{log(1+0.1)
-n = -7.000072677
n  = 7 years
Lastly, on the fourth, we need to solve for the rate, which is done using excel if we want an exact result and save time.
we list each value.
-250,000
 104, 087
 104, 087
 104, 087
And calculate IRR by selecting this values.
12.0%
