Annuities
The initial value of a loan (P) that will be paid with n installments of R dollars each is calculated as:
Where i is the adjusted interest rate:
And m is the number of payments per year.
We are given the data:
P = 2000
m = 121
n = 48
R = 49.30
Substituting:
This equation cannot be solved with a fixed formula or by isolating the unknown variable i.
We need to use successive approximations until we find a reasonable precision for the equation above.
Starting with the value:
i = 0.01, we get the equation: 2000 = 1872
For:
i = 0.005, we get the equation 2000 = 2099
i = 0.007, we get 2000 = 2004
i = 0.0071, we get 2000 = 1999
This value is close enough to produce an accurate answer, so:
i = 0.0071
Now calculate the APR:
Converting to % and rounding as required: APR = 8.5%