Question

A young engineer has a tax preparation company prepare her federal tax return. The company discovers that she is due a tax refund of $750. Since the company files the returns electronically, the engineer will receive her refund from the government in one month. However, the company offers to advance the engineer her money immediately if she pays a $35 filing fee today. What nominal and annual effective rates of return is the company earning for this “service”? (Ignore any fees paid for preparing the income tax return.)  

Answer 1

Refer the attached picture for the cash flow diagram

The cash flow can be written mathematically as follows

When we will discount the cash flow at the Internal rate of return then NPW = 0

Nominal rate = 4.8951% per month

Nominal rate = 4.8951 × 12 = 58.74% per annum

Effective rate = (1 + 0.048951)^12 -1 = 0.774445

Effective rate = 77.44% per annum.

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