Problem

Interest of $\$ 429.48$ was charged on a loan of $\$ 10^{\prime} 000$ for a 270 day period Calculate the interest rate.

Answer

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Answer

Converting this to percentage, we get the interest rate as approximately \(\boxed{5.81\%}\)

Steps

Step 1 :Given that the interest charged on a loan of $10,000 is $429.48 for a 270 day period, we are to calculate the interest rate.

Step 2 :The formula to calculate the interest rate is: \(\text{Interest Rate} = \frac{\text{Interest}}{\text{Principal}} / \text{Time}\)

Step 3 :In this case, the interest is $429.48, the principal is $10,000, and the time is 270 days.

Step 4 :However, the time should be in years for the interest rate to be in per annum terms. Therefore, we need to convert 270 days into years. Since there are approximately 365 days in a year, we can do this by dividing 270 by 365.

Step 5 :\(\text{Time in years} = \frac{270}{365} = 0.7397260273972602\)

Step 6 :Substituting the given values into the formula, we get: \(\text{Interest Rate} = \frac{429.48}{10000} / 0.7397260273972602 = 0.05805933333333334\)

Step 7 :Converting this to percentage, we get the interest rate as approximately \(\boxed{5.81\%}\)

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