Answer:
rate 20.86%
Explanation:
We will setp up the formula for an ordinary annuity
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 80000
time 7
rate = r
[tex]80000 \times \frac{1-(1+r)^{-7} }{r} = 281,660[/tex]
To solve we need to do it on excel, with the IRR function or estimate with try and error:
[tex]\frac{1-(1+r)^{-7} }{r} = 281,660/80,000[/tex]
The first part is the annuity factor with n = 7 we need to look into the PV table of an ordinary annuity which comes close to the quotient of 281,660/8,000 = 3,52075
at 20% = 3.605
at 21% = 3.508
The rate is between 20% and 21%
We now sart calculating the factor changing the decimals:
our target is: 3,52075
20.5% 3.5557
20.8% 3.5269
20.9% 3. 5174
Now the rate will be between 20.8%
and 20.9%
we start moving amoung the centimals
20.85% 3.5222
20.86 % 3.5212
20.87 % 3.5203
our target is: 3,52075
the IRR will be between 20.86% and 20.87%
we are almost there, we check if we need to round up or down:
our target is: 3,52075
20.865% 3.5207
20.864% 3.5208
20.866% 3.5206
It will be betwene 0.4 and 0.5 so it is better to round down.
We conclude the IRR is 20.86%
