Howard

[logistic_guy]

Howard invested \(\displaystyle \$ 67,945.16\) for \(\displaystyle 3\) years, \(\displaystyle 8\) months, and \(\displaystyle 17\) days in an account paying \(\displaystyle 8.19\%\) compounded daily using bankers’ rule. Find the total interest he will earn, both directly by using the nominal rate, and then by finding the effective rate and using it.

 

[logistic_guy]

Let us first calculate the future value by the compound interest formula taking into account that bankers’ rule means \(\displaystyle 360\) days in a year.

future value \(\displaystyle = P\left(1 + \frac{r}{n}\right)^{nt} = 67945.16\left(1 + \frac{0.0819}{360}\right)^{360\left(3 + \frac{8}{12} + \frac{17}{360}\right)} \approx 92096.21\)

 

[jonah2.0]

Beer drenched reaction follow.

Howard invested \(\displaystyle \$ 67,945.16\) for \(\displaystyle 3\) years, \(\displaystyle 8\) months, and \(\displaystyle 17\) days in an account paying \(\displaystyle 8.19\%\) compounded daily using bankers’ rule. ...

Where did you get this problem?

... Find the total interest he will earn, both directly by using the nominal rate, and then by finding the effective rate and using it.

In theory, they should be the same.

Let us first calculate the future value by the compound interest formula taking into account that bankers’ rule means \(\displaystyle 360\) days in a year.

future value \(\displaystyle = P\left(1 + \frac{r}{n}\right)^{nt} = 67945.16\left(1 + \frac{0.0819}{360}\right)^{360\left(3 + \frac{8}{12} + \frac{17}{360}\right)} \approx 92096.21\)

This should have a slightly larger amount.

 

[jonah2.0]

Beer drenched reaction follow.

Howard invested \(\displaystyle \$ 67,945.16\) for \(\displaystyle 3\) years, \(\displaystyle 8\) months, and \(\displaystyle 17\) days in an account paying \(\displaystyle 8.19\%\) compounded daily using bankers’ rule. Find the total interest he will earn, both directly by using the nominal rate, and then by finding the effective rate and using it.

Found it.
Biehler's book.

 

[jonah2.0]

Beer drenched reaction follow.

Let us first calculate the future value by the compound interest formula taking into account that bankers’ rule means \(\displaystyle 360\) days in a year.

future value \(\displaystyle = P\left(1 + \frac{r}{n}\right)^{nt} = 67945.16\left(1 + \frac{0.0819}{360}\right)^{360\left(3 + \frac{8}{12} + \frac{17}{360}\right)} \approx 92096.21\)

It would seem that thou art correct.

 

[logistic_guy]

Where did you get this problem?

In the bakery. If I buy 5 breads, I get one Finance problem free.

In theory, they should be the same.

What about now in the problem?

This should have a slightly larger amount.

Show me your calculations with this slightly larger amount!

Beer drenched reaction follow.

Found it.
Biehler's book.

Bravo patron jonah2.0

Beer drenched reaction follow.

It would seem that thou art correct.

 

[jonah2.0]

Beer drenched reaction follow.

In the bakery. If I buy 5 breads, I get one Finance problem free.

You don't say?
It would be nice if that bakery would also give out free beer as incentive for handing you an ambiguous task.

... What about now in the problem? ...

As I stated, they should be the same if you let your calculator do its voodoo in using the full expansion of your conversion. Since you seem so unsure (It's an even numbered exercise and there's no answer at the back section of your book), I can only imagine that you haven't combed through Biehler's examples and fine (& often humorous) explanations yet notwithstanding your claim of "refreshment". Or is this the first time you're reading his book?

... Show me your calculations with this slightly larger amount! ...

The problem was ambiguous to me since I haven't known that the bankers' rule can be extended to compound interest situations. So I imagined that this and that should be so and so.
Man this new beer brand I got sure makes me want to belt out a tune every few seconds.
All this money talk especially wants me to sing along with the Beatles.

... Bravo patron jonah2.0 ...

Don't thank me; thank the moon's (Google's) gravitational pull.

Have some beer refreshments and listen to good music.

 

[logistic_guy]

Sir jonah,

Let the verb \(\displaystyle \text{save}\) have past tense \(\displaystyle \text{sove}\) and past participle \(\displaystyle \text{soven}\).

Then,

You sove me while I was drowning. Since I was soven by the patron jonah, I have no place in this forum anymore.

It's either @Ted promote me to moderator, or I am leaving! I tried my best to keep this forum alive, but I got bored since your good friend Sir @lookagain stopped whining.

Where is the fun if @lookagain will be silent?

Gone the days when @harpazo made him crazy. I failed to make him crazy

He also has to apologize to professor @fresh_42.

Thanks a lot professor Jonah for the help and links you gave me. It's either @lookagain back again and keep whining or I am leaving for good.

 

[jonah2.0]

Beer drenched rambling/opinion/observation/reckoning ahead. Read at your own risk. Would be readers can take it seriously or take it with a grain of salt. In no event shall the wandering quixotic math knight-errant Sir jonah in his inebriated state (usually in his dead tired but mentally revived inebriated state) be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his "enhanced" beer (and tequila/absinthe) powered views.

Sir jonah,

Let the verb \(\displaystyle \text{save}\) have past tense \(\displaystyle \text{sove}\) and past participle \(\displaystyle \text{soven}\).

Then,

You sove me while I was drowning. Since I was soven by the patron jonah, I have no place in this forum anymore.

I disagree.
You do still have a place in this forum.
You can be a math knight-errant in this forum if you like; wandering as I do for lost souls like the fictional Senor Don Quixote did when he went insane.
You may take upon yourself to tackle other folks' math problems/troubles on your free time. Ah to aid the clueless, guide the lost, entertain them angry lazy ingrates, etc., in their struggle against our beloved queen. Queen to some of us, the dark Lord Mathematicus for a great unenlightened many. But I digress.

... It's either @Ted promote me to moderator, or I am leaving! ...

Quit joking around.
Have you actually applied to Ted to be a moderator?
If you have and your application was rejected, would you really leave over a minor issue?

... I tried my best to keep this forum alive, but I got bored since your good friend Sir @lookagain stopped whining.

Let me make myself clear in clear language in case you misunderstood: We are not good friends.
I do love how you annoy the lookagain unit though.

... Where is the fun if @lookagain will be silent?

You can still have fun in some other way.

... Gone the days when @harpazo made him crazy. I failed to make him crazy ...

No need to feel sad about that.

... He also has to apologize to professor @fresh_42. ...

That will never happen; the lookagain unit has a big bug up its butthole.
The lookagain unit needs to drink lots of alcohol to kill that bug.
You don't need worry about fresh_42's jousting with the lookagain unit; fresh_42 can take care of himself.

... Thanks a lot professor Jonah for the help and links you gave me. ...

No worries.

... It's either @lookagain back again and keep whining or I am leaving for good.

Come on; don't be like that.
Would you really leave me all alone here over the lookagain unit non participation and whining.
I must confess that I rather enjoyed your posts lately; especially them accounting posts. They are definitely refreshing to say the least. One key to annoying the lookagain unit is apparently through vulgarity. Mention of buttholes will definitely solicit a few high blood induced reaction from the lookagain unit. Don't leave. I love you man!

 

[logistic_guy]

CheersSir jonah2.0


Let us go back to the problema Finanziario.

The total interest Howard will earn is:

\(\displaystyle 92096.21 - 67945.16 = 24151.05\)

 

[jonah2.0]

Beer drenched reaction follow.

CheersSir jonah2.0
View attachment 39174

Let us go back to the problema Finanziario.

The total interest Howard will earn is:

\(\displaystyle 92096.21 - 67945.16 = 24151.05\)

Agreed. For now.
Biehler's book examples strongly suggest that path but still need to comb through his book, if I ever find the energy and motivation to do it, to convince myself of that particular bankers' rule extension to compound interest.

P.S. Any idea on why your posts are getting a ton of views from 7K upwards?

 

[logistic_guy]

P.S. Any idea on why your posts are getting a ton of views from 7K upwards?

If you type the word math in google and you get this website as the first result, what does this mean? Tons of visitors will enter here, so it is typical to get \(\displaystyle 7\text{k}\) and more.

They should give me a noble prize as one of the reasons that this website is being in the top is because of my \(\displaystyle 1000\) posts.

 

[jonah2.0]

Beer drenched reaction follow.

...
The total interest Howard will earn is:

\(\displaystyle 92096.21 - 67945.16 = 24151.05\)

Confirmed according to Biehler.
Furthermore,

Howard invested \(\displaystyle \$ 67,945.16\) for \(\displaystyle 3\) years, \(\displaystyle 8\) months, and \(\displaystyle 17\) days in an account paying \(\displaystyle 8.19\%\) compounded daily using bankers’ rule. Find the total interest he will earn, both directly by using the nominal rate, and then by finding the effective rate and using it.

For part 2, specifically

..., and then by finding the effective rate and using it.

Without rounding, total interest earned using the effective rate \(\displaystyle w\) is identical to total interest using the nominal rate. With rounding, you get

 

[logistic_guy]

Confirmed according to Biehler.

According to Biehler!! Do you mean that he has the solutions to the even problems?

Without rounding, total interest earned using the effective rate \(\displaystyle w\) is identical to total interest using the nominal rate. With rounding, you get

What you have shown with \(\displaystyle \text{Desmos}\) was wonderful. But I think that the aim of the exercise is to round.

My calculations for the effective rate is:

effective rate \(\displaystyle = \left(1 + \frac{0.0819}{360}\right)^{360} - 1 \approx 0.0853 = 8.53\%\)

It matches yours. And I wanna say this about you: you're such a Gold Sir jonah\(\displaystyle 2.0\) who was just discovered recently. If I was the head of the chemists community, I would replace \(\displaystyle \text{Au}\) with \(\displaystyle \text{Jo}\) in the periodic table in honor of the professor jonah\(\displaystyle 2.0\).

And later, I will insist to make them write it as \(\displaystyle \text{Jo}2.0\)

 

[logistic_guy]

For the sake of completeness, let me do the second part of the problem where I use the effective rate.

future value \(\displaystyle = 67,945.16(1 + 0.0853)^{3+\frac{8}{12}+\frac{17}{360}} = 92084.50\)

The total interest Howard will earn in this case is:

\(\displaystyle 92084.50 - 67945.16 = 24139.34\)