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Question 8 of 10

If an 11-day single payment loan has a periodic interest rate of 9.3%, what is
the approximate effective interest rate of the loan?
A. 1812.0%
B. 19,120.0%
C. 18,120.0%
D. 1912.0%

User Teuta
by
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1 Answer

5 votes

Final answer:

To find the effective interest rate for an 11-day loan with a periodic rate of 9.3%, we annualize the rate using the formula [(1 + i)^(365/t)] - 1, resulting in an effective annual rate of approximately 1912.0%.

Step-by-step explanation:

The subject of this question is related to the concept of effective interest rates in financial mathematics.

To approximate the effective interest rate of a loan with a given periodic interest rate, we need to annualize the rate because the loan period is less than a year (in this case, 11 days). The formula to annualize a periodic interest rate (i) for a loan period (t) in days is:

Effective Interest Rate = [(1 + i)^(365/t)] - 1

For a loan with a periodic interest rate of 9.3% (or 0.093) for 11 days, the effective annual rate is:

[(1 + 0.093)^(365/11)] - 1

Doing the calculation:

[(1.093)^(33.1818)] - 1 ≈ 1912.0%

Therefore, the approximate effective interest rate of the loan is 1912.0%, which corresponds to answer choice D.

User Tobias Glaus
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