Question

Western Sky Financial LLC offers a "Problem Solver" Loan where you can get up to $10,000 in one day, without collateral. The typical $10,000 loan has an upfront fee of $75 (thus you really only get $9,925) and is repaid in 84 monthly payments of $743.49. Assume that compounding is monthly. What is the monthly rate for this loan? What is the APR for this loan (it is important to note that APR legally REQUIRES the calculation to include any fees charged for the loan, thus in this case, the APR would be calculated after subtracting the fee. Thus, the present value of the loan is really only $9,925)? What is the effective annual rate for the loan?

Answer 1

Answer:

monthly rate = 7.47%

APR:89.64%

effective rate 137%

Explanation:

We will calculate the monthly rate:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C       743

time 84 months

rate           r

PV $9,925.0000

$743.49 \times \frac{1-(1+r)^{-84} }{r} = 9,925$

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

$\frac{1-(1+r)^{-84} }{r} = 13.34920$

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:

$(1+0.0747)^{12} = (1+r_e)$

effective rate = 1.373815638 = 137%