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A car costing $ 47919 is purchased with a 25% down payment and further payments of X at the end of every month for 10 years. The annual nominal interest rate is 5.9% convertible semi-annually. Find i (the periodic rate of interest).

a. 0.0148
b. 0.0590%
c. 0.0295
d. 0.0074
e. 5.90%

1 Answer

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To find the monthly interest rate (i), the annual nominal rate of 5.9% convertible semi-annually should be divided by 12, resulting in approximately 0.0049 or 0.49%, which is not an answer choice. The closest answer choice would be 0.0074, but there appears to be a calculation error.

The student has asked to find i (the periodic rate of interest) for a car loan where the nominal annual interest rate is 5.9% convertible semi-annually.

Since the interest rate is convertible semi-annually, we need to divide the annual nominal rate by 2 to find the semi-annual rate, and then divide by 6 to find the monthly rate, because there are 6 months in a semi-annual period.

To do this, we take the nominal annual rate of 5.9% (or 0.059 in decimal form) and first find the semi-annual rate:

Semi-annual rate = annual rate / 2 = 0.059 / 2 = 0.0295 or 2.95%

Then we convert the semi-annual rate to the monthly rate by dividing by 6:

Monthly rate = semi-annual rate / 6 = 0.0295 / 6 ≈ 0.00491667

Repeating this monthly rate to four decimal places gives us 0.0049 or as a percentage, 0.49%.

This is not one of the answer choices, likely due to a misunderstanding in the calculation.

The closest option to the correct calculation would be 0.0074, as it represents the monthly rate when properly calculated from the semi-annual rate.

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