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 * (Tenure in months)/(Months in a year)`

`Discount on Note = 16 * 0.08 * (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 = (Interest)/(Loan amount)`

`Seven month Interest Rate = (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 * (12)/(7)`

`Sky's Effective Interest Rate = 0.048951049* (12)/(7)`

`Sky's Effective Interest Rate = 0.083916084`