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 for this short term loan?

Introduction / Context:
This question illustrates an extremely high interest rate charged over a very short period, which is then converted to an annual rate using simple interest. The loan shark lends 100 dollars and demands 120 dollars after one month, representing a large one month interest. The problem shows how apparently small short term loans can correspond to huge annual percentage rates when scaled up.

Given Data / Assumptions:
- Principal P = 100 dollars. - Amount repaid after one month A = 120 dollars. - Time T for the loan = 1 month. - Interest is calculated using simple interest, not compounding. - Required quantity is the equivalent annual rate of interest R percent per annum.

Concept / Approach:
First find the one month simple interest as A − P. Then compute the monthly simple interest rate as (interest for one month) divided by principal, expressed in percent. Under simple interest, the annual rate is obtained by multiplying the monthly rate by 12, because interest grows linearly with time. This scaling from monthly to yearly rate is valid since no compounding is assumed.

Step-by-Step Solution:
Step 1: Compute one month interest: SI month = A − P = 120 − 100 = 20 dollars. Step 2: Monthly rate r month (in percent) is (SI month * 100) / P. Step 3: Substitute values: r month = (20 * 100) / 100 = 20 percent per month. Step 4: Under simple interest, annual rate R = monthly rate * 12. Step 5: Compute R = 20 * 12 = 240 percent per annum. Step 6: Therefore, the equivalent annual rate is 240 percent per year.

Verification / Alternative check:
We can also treat the annual rate R as unknown in the simple interest formula. For one month, which is 1 / 12 of a year, SI should be 20 dollars. Using SI = (P * R * T) / 100 with P = 100, T = 1 / 12, we get 20 = (100 * R * (1 / 12)) / 100. This simplifies to 20 = R / 12. Multiplying both sides by 12 gives R = 240 percent, confirming the earlier calculation.

Why Other Options Are Wrong:
A rate of 210 percent would give a monthly equivalent of 210 / 12 = 17.5 percent and only 17.50 dollars of interest, not 20 dollars. A rate of 220 percent corresponds to about 18.33 percent per month, again too low. A rate of 230 percent gives roughly 19.17 percent per month, still not enough to produce 20 dollars interest on 100 dollars in one month. Only 240 percent per annum corresponds exactly to a 20 percent monthly simple interest rate.

Common Pitfalls:
Learners might assume a compounding interpretation and incorrectly raise (1 + monthly rate) to a power, which is not required here. Others may forget to convert months to a fraction of a year when using the simple interest formula. Remember that for simple interest, the annual rate scales linearly with time, so multiplying the monthly rate by 12 is valid.

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