Question

You are expecting a tax refund of $1,000 in 10 weeks. A tax preparer offers you an "interest-free" loan of $1,000 for a fee of $50 to be repaid by your refund check when it arrives in 10 weeks. Thinking of the fee as interest, what simple interest rate would you be paying on this loan? (Round your answer to three decimal places.)

Answer 1

26% per annum

Step-by-step explanation:

Data provided:

Expected tax refund = $1,000

Time = 10 weeks =
`\frac{\textup{10}}{\textup{52}}` = 0.192 year (1 year = 52 weeks)

Loan amount = $1,000

Loan fee = $50

Now,

The simple interest is calculated as:

Interest = Principle × Rate × Time

considering $50 as interest

we have

$50 = $1,000 × Rate × 0.192

or

Rate = 0.26

or

Rate = 0.26 × 100% = 26% per annum

Hence,

The simple interest rate paid on the loan is 26% per annum