Respuesta :
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
[tex]Discount on Note = Face Value * Discount Rate * \frac{Tenure in months}{Months in a year}[/tex]
[tex]Discount on Note = 16 * 0.08 * \frac{7}{12}[/tex]
[tex]Discount on Note = 0.746666667million[/tex]
[tex]Loan Amount received by Sky = Face Value - Discount on note[/tex]
[tex]Loan Amount received by Sky = 16 - 0.746666667[/tex]
[tex]Loan Amount received by Sky = 15.25333333 million[/tex]
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:
[tex]Seven month Interest Rate = \frac{Interest}{Loan amount}[/tex]
[tex]Seven month Interest Rate = \frac{0.746666667}{15.25333333}[/tex]
[tex]Seven month Interest Rate = 0.048951049[/tex]
From this we can work out the effective interest rate for Sky as follows:
[tex]Sky's Effective Interest Rate = Seven month interest rate * \frac{12}{7}[/tex]
[tex]Sky's Effective Interest Rate = 0.048951049* \frac{12}{7}[/tex]
[tex]Sky's Effective Interest Rate = 0.083916084[/tex]
