Question

Many tax preparation firms offer their clients a refund anticipation loan (RAL). For a fee, the firm will give a client his refund when the return is filed. The loan is repaid when the Internal Revenue Service sends the refund directly to the firm. Thus, the RAL fee is equivalent to the interest charge for a loan. The schedule in the table on the right is from a major RAL lender. Use this schedule to find the annual rate of interest for a $4,700 RAL, which is paid back in 33 days. RAL Amount $0-$500 $501 $1,000 $1,000 - $1,500 $1,501-$2,000 $2,001- $5,000 RAL Fee $29.00 $39.00 $49.00 $69.00 $89.00 (Assume a 360-day year.) What is the annual rate of interest for this loan? % (Round to three decimal places.)

Answer 1

We can see here that the annual rate of interest for the $4,700 RAL, which is paid back in 33 days, is approximately 20.625%.

To calculate the annual rate of interest for a $4,700 refund anticipation loan (RAL) that is paid back in 33 days, we can use the formula for calculating annual interest rate:

Annual Interest Rate = (RAL Fee / RAL Amount) × (360 / Number of Days)

In this case, the RAL fee for a $4,700 RAL falls within the range of $2,001-$5,000, which has a fee of $89. Therefore, the RAL fee is $89.

Inputting the values into the formula:

Annual Interest Rate = (89 / 4700) × (360 / 33)

Simplifying the equation:

Annual Interest Rate ≈ 0.018936 × 10.9091

Annual Interest Rate ≈ 0.206250756

Converting to a percentage:

Annual Interest Rate ≈ 20.625%

Therefore, the annual rate of interest for the $4,700 RAL, which is paid back in 33 days, is approximately 20.625%.