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Dominik [7]
3 years ago
6

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:
Business
1 answer:
mash [69]3 years ago
4 0

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

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