Advanced Math/Proceeds

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Expert: - 7/13/2009


Question
On June 30, 2007, Simon Company discounted a customer’s $180,000, 6-month, and 10 percent note receivable dated April 30, 2007. A discount rate of 12 percent was charged by the bank. Simon’s proceeds from this discounted note would be: This is my working please tell me what i am doing wrong:
Maturity = 180,000 (1 + 0.1 * 6/12)
(180,000(1.05) = 189.000
Discount = 6 - 3 = 3
Bank Discount = 189,000 x 0.12 * 3/12 = 5,670
Proceeds = 189,000 - 5,670 = 183,330  

Answer
Maturity
What you did was calculate the amount of interest paid at the time of maturity.  However, only 2 months have passed.  This means that the original amount should be multiplied by (1 + 0.1*2/12).
Then $180,000(0.2/12) = $3,000 is the interest at that point.

Discount
The effective interest is d/(1-d) where d is the discount rate.
This would be 0.12/(1-.12) = 0.136363636 (=3/22).
This would mean to find the discount rate, I belive the interest at this point should be multiplied by 3/22.  This gives $409.

For discount rates, see http://en.wikipedia.org/wiki/Discount_rate

Bank Discount
I can see that comes from line 3, which I had a question on.
As noted in the discount paragraph before, the discount rate and the interest rate are related to each other, but are not the same.

Proceeds
The proceeds should be the base amount + interest for only 2 months
- penalty for early withdrawl.

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What I think needs to be done is since the $180,000 was in the bank for 2 months (May and June), the interest would only be
$180,000*2*10%/12 = $3,000, so the money at that point would be $183,000.

However, there is also a 12 percent discount rate charged by the bank.  This should apply to the interest earned as a fee on the amount at 12%.  Since it is a discount rate, that means that the effective interest rate is, as found above, is 3/22.  When multiplied by the amount at that point, the result is $409.

Thus, the amount paid out should be $183,000 - $409 = 182,591.
That would be an overall effective interst rate of only 8.37%, instead of the rate of 10%.

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I believe that the discount rate was charged only on the interest, but it may be on the full amount.  In this case, the discount rate would be $183,000 * 12%*2/12 = $3,630.  In this case, the person doing the early withdrawl would have lost $630 dollars overall.  

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