A 150-day note will mature for $100,000. It is sold 102 days before maturity for $98200. What rate of simple discount p.a. was used?
i get the answer 13.94% but when i plug it back into the equation i get 98,166.79 not 98,200 what have i done wrong?
i get the answer 13.94% but when i plug it back into the equation i get 98,166.79 not 98,200 what have i done wrong?
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The tricky part of these is to figure out how to express a year.
If a year is figured on 360 days, then the selling price for a simple discount rate of d is
100000 (1-102d/360) = 98200
1800 = 10200000d/360
d = 0.06352941176470588235294117647059 or 6.35294%
Since the discount is 1800/100000 = 1.8% over 102/360 = .2833333 years
1.8%/.2833333 = 6.35294%
Or you can use proportions to figure it:
1.8/102 = d/360
d = 360x1.8/102 = 6.35294
You'll get a slightly different answer if you use 365 instead of 360. Actual practice varies.
13.94% is way too big. Any simple estimate will tell you that's out of line.
The fact that it's a 150 day note is irrelevant. All you need is the number of days remaining to maturity, and the selling price.
If a year is figured on 360 days, then the selling price for a simple discount rate of d is
100000 (1-102d/360) = 98200
1800 = 10200000d/360
d = 0.06352941176470588235294117647059 or 6.35294%
Since the discount is 1800/100000 = 1.8% over 102/360 = .2833333 years
1.8%/.2833333 = 6.35294%
Or you can use proportions to figure it:
1.8/102 = d/360
d = 360x1.8/102 = 6.35294
You'll get a slightly different answer if you use 365 instead of 360. Actual practice varies.
13.94% is way too big. Any simple estimate will tell you that's out of line.
The fact that it's a 150 day note is irrelevant. All you need is the number of days remaining to maturity, and the selling price.