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------------------------------------------------ Find both the exact and ordinary interest on $30,700 at 13 1/4% for 141 days. Then find the amount by which the ordinary interest is larger.

1) What is the exact interest on $30,700 at 13 1/4% for 141 days?

2) What is the ordinary interest on $30,700 at 13 1/4% for 141 days?

3) By how much is the ordinary interest larger than the exact interest?

Answer :

1) The exact interest on $30,700 at 13 1/4% for 141 days is $1,609.01.

To calculate the exact interest, we need to use the formula: Exact Interest = Principal × Rate × Time.

In this case, the principal is $30,700, the rate is 13 1/4% (or 0.1325 as a decimal), and the time is 141 days converted to years (141/365 ≈ 0.3863).

Exact Interest = $30,700 × 0.1325 × 0.3863 = $1,609.01 (rounded to two decimal places).

2) The ordinary interest on $30,700 at 13 1/4% is $1,579.79.

To calculate the ordinary interest, we use the formula: Ordinary Interest = Principal × Rate × Time.

Since the time is given in days, we don't need to convert it to years.

Ordinary Interest = $30,700 × 0.1325 × 141/365 = $1,579.79 (rounded to two decimal places).

3) The amount by which the ordinary interest is larger is $29.22.

To find the difference between the exact and ordinary interest, we subtract the exact interest from the ordinary interest.

Difference = Ordinary Interest - Exact Interest

Difference = $1,579.79 - $1,609.01 = -$29.22 (rounded to two decimal places).

The negative sign indicates that the exact interest is larger than the ordinary interest.

The exact interest on $30,700 at 13 1/4% for 141 days is $1,609.01, the ordinary interest is $1,579.79, and the amount by which the ordinary interest is larger is $29.22.

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