Answer:
monthly rate = 7.47%
APR:89.64%
effective rate 137%
Explanation:
We will calculate the monthly rate:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 743
time 84 months
rate r
PV $9,925.0000
[tex]743.49 \times \frac{1-(1+r)^{-84} }{r} = 9,925\\[/tex]
We solve this using excel or a financial calculator for a precise solution
0.074734946
another way we do so: 9975/743.49 = 13.34920
And we look into an annuity table for which rate generates a factor of 13.416 when time = 84
as this time is not in the table, we are better off doing excel solution
another way will be trial and error, we enter different rates until we are satisfied with the margin of error
[tex] \frac{1-(1+r)^{-84} }{r} = 13.34920\\[/tex]
we will try 5% 6% 7% 8 % and so on until we get closer. In this case
using 7.5% we got: 13.3027
using 7.4% we got: 13.4799
So the answer (13.34920) is between these two,
we now add a centecimal:
if r = 7.45 then factor = 13.3907
if r = 7.46 then factor = 13.3730
if r = 7.47 then factor = 13.3554
if r = 7.48 thenb factor = 13.3378
so we could say the rate will be 7.47% using trial and error.
APR:
as the year has 12 months, then 7.47x12 will be the APR
7.47 x 12 = 89.64%
Effective rate:
In this case we have t oconvert the montly compounding rate to an annual rate compounding annual:
[tex](1+0.0747)^{12} = (1+r_e)[/tex]
effective rate = 1.373815638 = 137%
