Question

On october 31, 2009, sky co. borrowed $16 million cash and issued a 7-month, noninterest-bearing note. the loan was made by star finance co. whose stated discount rate is 8%. sky's effective interest rate on this loan is:

Answer 1

Answer: Sky's effective interest rate on this loan is 8.39%.

In this question, we assume that interest is compounded annually.

Since Sky issues a non-interest bearing note, Star Finance will deduct 7 months' interest at 8% on the Face Value of the loan and pay the rest as principal to Sky.

Face value of the note            $16 million

Discount Rate p.a                        8%  

Tenure of the note                    7 months

$Discount on Note = Face Value * Discount Rate * \frac{Tenure in months}{Months in a year}$

$Discount on Note = 16 * 0.08 * \frac{7}{12}$

$Discount on Note = 0.746666667million$

[tex]Loan Amount received by Sky = Face Value - Discount on note[/tex]

$Loan Amount received by Sky = 16 - 0.746666667$

$Loan Amount received by Sky = 15.25333333 million$

So, Sky pays an interest of 0.746666667 on a sum of 15.25333333  for 7 months. This works out to a seven month interest of:

$Seven month Interest Rate = \frac{Interest}{Loan amount}$

$Seven month Interest Rate = \frac{0.746666667}{15.25333333}$

$Seven month Interest Rate = 0.048951049$

From this we can work out the effective interest rate for Sky as follows:

$Sky's Effective Interest Rate = Seven month interest rate * \frac{12}{7}$

$Sky's Effective Interest Rate = 0.048951049* \frac{12}{7}$

$Sky's Effective Interest Rate = 0.083916084$