Part 1:
Data Available = one-week loans at 7% interest per week
Percentage Return also is known as Annual Percentage Return is calculated as
APR = r * m
r = interest rate
m = frequency of compunding
Hence APR = 7% * 52
= 364%
EAR = (1 + (stated annual interest rate)/ m ) ^m-1
= (1 + 364/(52*100))^52 - 1
= 33.7253 - 1
= 32.7253
Part 2: To calculate APR and EAR for discounted interst rate
Effective rate = (discounted interest rate) / (100 - 100* discounted intereest rate)
= 0.07/(1 - 0.07) = 0.0752 = 7.52%
Hence APR = 7.52 * 52 = 391.39
EAR = (1 + (stated annual interest rate)/ m ) ^m-1
= (1 + 391.39/(52*100))^52 - 1
= 43.39 - 1
= 42.39
Part 3
Total amount to be repaid = 260 USD
Weekly instalment = 65 USD
Effective value of the loan taken = 179.19 USD
Interest paid = 80.81 USD. Yearly interest paid = 969.72
Average Loan Balance = 179.19/2 = 89.895
EAR = 969.72 / 89.89 = 1078.78 %
EAR = (1 + (stated annual interest rate)/ m ) ^m-1
1078.78 = (1 + APR/(52*100))^52 - 1
APR = (1078.78 + 1) ^ (1/52) - 1
= (1.1437 - 1) * 52
= 14.37% * 52
= 747.5331%
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