A loan shark lends $100 to a borrower who agrees to repay $120 at the end of one month. Assuming simple interest, what is the equivalent annual rate of interest (in percent per annum)?

Introduction / Context:
This problem illustrates extremely high interest rates often associated with informal or predatory lending. The borrower repays more than the principal in just one month, and the task is to convert this monthly interest into an equivalent annual simple interest rate.

Given Data / Assumptions:

• Principal, P = $100.
• Amount repaid after 1 month, A = $120.
• Time period, T = 1 month.
• Interest is assumed to follow simple interest for conversion to annual rate.

Concept / Approach:
First we compute the interest for one month by subtracting the principal from the amount repaid. Then we find the monthly rate as a percentage of the principal. Finally, we convert this monthly rate into an annual rate of simple interest by multiplying by 12, because there are 12 months in a year. The key formulas are:
Interest for period = A - PRate for period (percent) = (Interest / P) * 100

Step-by-Step Solution:
Step 1: Compute the simple interest for one month.SI (1 month) = A - P = 120 - 100 = $20Step 2: Find the monthly rate as a percentage.Monthly rate = (20 / 100) * 100 = 20%Step 3: Convert the monthly rate to an annual rate under simple interest.Annual rate = Monthly rate * 12Annual rate = 20% * 12 = 240%

Verification / Alternative check:
As a rough check, if the annual simple interest rate is 240%, then yearly interest on $100 is $240. For one month, under simple interest, the fraction of the year is 1 / 12, so the interest would be 240 * (1 / 12) = $20, which matches the interest charged. This confirms that 240% is the correct equivalent annual simple interest rate.

Why Other Options Are Wrong:

• 210%, 220%, and 230% correspond to monthly rates of 17.5%, 18.33%, and 19.17% respectively when divided by 12, none of which yield exactly $20 interest on a $100 loan in one month.
• Only 240% produces a monthly interest rate of 20% that matches the given repayment terms.

Common Pitfalls:
Learners may mistakenly treat the 20% monthly rate as directly equal to the annual rate, forgetting to multiply by 12. Another common error is to interpret 20 as a rate instead of $20 interest, or to use compound interest ideas even though the question is asking for a simple interest equivalent. Always remember that for simple interest the annual rate scales linearly with time, so monthly rate times 12 gives the annual rate.

Final Answer:
The equivalent annual simple interest rate charged by the loan shark is 240% per annum.