Answer:
APR = 0.078125607
APR = 7.81%
Explanation:
We will calculte the rate of an annuity of 1,500 for 72 months which present value euqalt to 86:
[tex]PTM \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
PTM $ 1,500
time 72 years
PV $ 86,000
[tex]1,500 \times \frac{1-(1+r)^{-72} }{r} = 86,000\\[/tex]
We will solve it using excel with the "goal seek" tool
or a financial calculator:
IRR = 0.006510467 per month we multiply by 12 to get the APR
APR = 0.078125607
At hand, we could also solve with trial and error:
we will do:
[tex]\frac{1-(1+r)^{-72} }{r} = 86,000\div 1,500\\[/tex]
We will look for r values which get us closer to the factor value of the IRR
factor: 86,000 / 1,500 = (57 + 1/3)
for example If we use 0.0065 the factor is:
[tex]\frac{1-(1+0.0065)^{-72} }{0.0065}= 57.3534 [/tex]
for 0.0066 will be:
[tex]\frac{1-(1+0.0066)^{-72} }{0.0066}= 57.1618 [/tex]
As one value is avbove and another is below we can indicate that the rate is between these two values. We can keep looking adding more decimals or be conformed with this margin of error
we pick 0.0065 and multiply by 12 to get the APR: 0.078 Which is close tothe excel value
