QuestionJuly 20, 2025

If you paid 78 to a loan company for the use of 1,410 for 41 days, what annual rate of interest did they charge? (Assume a 360-day year.) The annual rate of interest is square % (Round to three decimal places.)

If you paid 78 to a loan company for the use of 1,410 for 41 days, what annual rate of interest did they charge? (Assume a 360-day year.) The annual rate of interest is square % (Round to three decimal places.)
If you paid 78 to a loan company for the use of 1,410 for 41 days, what annual rate of interest did they charge? (Assume a 360-day year.)
The annual rate of interest is square %  (Round to three decimal places.)

Solution
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Answer

The annual rate of interest is 48.947\%. Explanation 1. Calculate the daily interest rate Use the formula for simple interest: I = P \times r \times t, where I is interest, P is principal, r is rate, and t is time. Rearrange to find r: r = \frac{I}{P \times t}. Here, I = 78, P = 1410, and t = 41 days. 2. Calculate the annual interest rate Convert the daily rate to an annual rate by multiplying by 360 (days in a year): r_{\text{annual}} = r_{\text{daily}} \times 360.

Explanation

1. Calculate the daily interest rate<br /> Use the formula for simple interest: $I = P \times r \times t$, where $I$ is interest, $P$ is principal, $r$ is rate, and $t$ is time. Rearrange to find $r$: $r = \frac{I}{P \times t}$. Here, $I = 78$, $P = 1410$, and $t = 41$ days.<br /><br />2. Calculate the annual interest rate<br /> Convert the daily rate to an annual rate by multiplying by 360 (days in a year): $r_{\text{annual}} = r_{\text{daily}} \times 360$.
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