Bonus points: if true, this would mean it has a simple interest rate of 33.48%. the only fees associated are $20/mo or $240 a year. What causes the discrepancy between the APR and Simple Interest Rate?

From my understanding, the APR should be 34.28% in this situation, not 59.9%.

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APR (given by the lender) is 59.9% (this is including all fees and is not the interest rate)

credit limit is $30,000

Term is 1 year

52 payments

PMT = (PV × (r ÷ n)) ÷ (1-(1 r ÷ n) ^ (-n × t)

where r= APR, PV = present value and n = number of periods, t = term length

r= 59.9

PV = 30,000

n = 52

t = 1

PMT = (30000 × (59.9 ÷ 52)) ÷ (1-(1 59.9 ÷ 52)-52×1 = $770.08

If the payment is $770.08 for 52 weeks then the total payback is $40,044.11 and the simple interest is $10,044.11

therefore

a = 40,044.11 i = 10,044.11

er = (1/ t)÷ (a ÷ PV - 1) = ((1÷1) × (40,044.11 ÷ 30,000 - 1) = 33.4804% per year

or

er = (100 × i) ÷ (PV * t) = (100 × 10,044.11) / (30,000 * 1) = 33.4804% per year

the ONLY fees associated with the line of credit is a $20 monthly maintenance fee so $240 annually.

I am told that the explanation for the discrepancy is because the number of payments per year messes up the APR calculation, but the APR calculation does not take into account the number of payments per year

APR = ((Interest Fees / Loan amount) / Number of days in loan term)) x 365 x 100

((10,044.11 240 / 30,000) / 365)) x 365 x 100 = 34.28% APR

However, the APR is, without a doubt, 59.9%

I also do not understand why we use the APR to calculate the PMT then switch to the simple interest rate for everything else..

For example, if we use the APR in any FV formulas we get:

FV = PV × (1 r × t) = 30,000 × ( 1 .559 × 1) = $47,970

or

FV = PV × (1 r × t) = 30,000 × ( 1 (.559/52) ⁵² = $54,422

but if we swap the APR for the Simple interest rate we get the "correct" answer

FV = PV × (1 r × t) = 30,000 × ( 1 .334803 × 1) = $40,044.11

So from my end, it appears that if the loan will be paying back $770.08 per week for 52 weeks giving a total payback of $40,044.11 and at the same time the APR is 59.9%. There must be between $7925.89 and $14,377.89 in hidden fees