Many tax preparation firms offer their clients a refund anticipation loan (RAL).
ID: 2546154 • Letter: M
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 $2,036 RAL, which is paid back in 34 days.
RAL Amount
RAL Fee
$0 - $500
$29.00
$501 - $1,000
$39.00
$1,000 - $1,500
$49.00
$1,501 - $2,000
$69.00
$2,001 - $5,000
$89.00
(Assume a 360-day year.)
What is the annual rate of interest for this loan? ________%
(Round to three decimal places.)
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 $2,036 RAL, which is paid back in 34 days.
RAL Amount
RAL Fee
$0 - $500
$29.00
$501 - $1,000
$39.00
$1,000 - $1,500
$49.00
$1,501 - $2,000
$69.00
$2,001 - $5,000
$89.00
(Assume a 360-day year.)
What is the annual rate of interest for this loan? ________%
(Round to three decimal places.)
Explanation / Answer
The calculations are done under two assumptions; 1) The RAL fee is paid after 34 days 2) The RAL fee is deducted from the RAL amount. The annual interest rate is also calculated with and without compounding in each case. 1) The interest rate for 34 days (assuming it is paid at the end of 34 days) = (89/2036) = 4.37% The annual simple interest rate would be = (89/2036)*(360/34)= 46.28% [a] The annual effective interest rate (with compounding) = (1+89/2036)^(360/34)-1 = 57.30% [b] 2) The interest rate for 34 days (assuming it is deducted upfront from the RAL) = (89/1947) = 4.57% The annual simple interest rate would be = (89/1947)*(360/34)= 48.40% [c] The annual effective interest rate (with compounding) = (1+89/1947)^(360/34)-1 = 60.52% [d]