1. Ah, financial formulas, the only kind of math that can make money disappear faster than a magician. Anyway, let's tackle this promissory note puzzle, shall we?
To find the proceeds at the time of the sale, we need to subtract the discount from the face value of the note. So, let's do some mathemagics:
Discount = Face Value * Discount Rate * Time
= $12,000 * 0.095 * (30/365) [since August 30 - July 14 = 47 days, but we're only interested in 30 days]
Proceeds = Face Value - Discount
= $12,000 - ($12,000 * 0.095 * (30/365))
And voila! You've got your answer. Now, if only we could use these funny formulas to calculate the value of a clown nose, life would be much simpler.
2. Time for another financial exploration! Let's grab our calculators and dive into the world of T-bills.
(a) To find the purchase price of the T-bill, we need to calculate the discount:
Discount = Face Value * Discount Rate * Time
= $15,000 * 0.0385 * (16/52) [since 16 weeks is a fraction of a year]
Purchase Price = Face Value - Discount
= $15,000 - ($15,000 * 0.0385 * (16/52))
(b) The maturity value of the T-bill is simply the face value:
Maturity Value = Face Value = $15,000
(c) To calculate the interest earned, we subtract the purchase price from the face value:
Interest Earned = Face Value - Purchase Price
= $15,000 - [($15,000 * 0.0385 * (16/52))]
(d) Now, for the effective rate of interest, we need to put our thinking caps on:
Effective Rate of Interest = (Interest Earned / Purchase Price) * (365 / Time)
= [(Face Value - Purchase Price) / Purchase Price] * (365 / Time)
= [(15,000 - (15,000 * 0.0385 * (16/52))) / (15,000 * 0.0385 * (16/52))] * (365 / (16/52))
Now, you've got all the pieces of the financial puzzle! Enjoy crunching those numbers and may the interest rates be ever in your favor. Or at least, not against you.