Kyle Estimates that his business in growing at a rate of 5% per year. HIs profits in 2005 were $67000. Estimate the profits in 2010.

Question

anonymous · Answer

Is it along the same lines?

johnweldon1993 · Answer

okay so we have exponential growth this time...meaning 1 + rate...so yeah basically the same thing

johnweldon1993 · Answer

so you have the inital
the rate
the time

all you need

so the equation would look like?

anonymous · Answer

67000(1.05)^t?

johnweldon1993 · Answer

correct...but what is t?

anonymous · Answer

Oh the answer- 85510.87

mathslover · Answer

Yep I got it...

johnweldon1993 · Answer

there we go!

mathslover · Answer

67000 * (1.05)^5 u r right @zaynahf

johnweldon1993 · Answer

yup...that would be correct @mathslover and @zaynahf

mathslover · Answer

$ 85110.864

anonymous · Answer

I have a slightly different formula:
$$A= P (1+\frac{r }{ n })^{n \times t}$$
where r is the rate, n is the time, P is the principle amount and n is the # of times compounded

Do i need to insert the n value?

mathslover · Answer

n = 5?

anonymous · Answer

wait sorry, t is time

johnweldon1993 · Answer

that would be if it was compounded at a different rate i believe...like if it was quarterly

johnweldon1993 · Answer

i believe anyways

mathslover · Answer

Oh yeah @johnweldon1993 is right, compounded annually ...

johnweldon1993 · Answer

since we only wanted annually....we didn't need to account for "n" like in that equation

mathslover · Answer

n = 1 ...

johnweldon1993 · Answer

so imagine "N" was number of times per year the money got accounted for...in this case...since it is annually...n would = 1

mathslover · Answer

Agreed.^

anonymous · Answer

So if i had an investment of 4000 at 4.5% interest compounded quarterly for 5 years
would it be:
$$A= 4000(1+\frac{ .045 }{ 3 })^{3(5)}$$

anonymous · Answer

Im confused what i would put for n in that case

johnweldon1993 · Answer

umm quarters in the year....i think it would be 4 quarters in the year....in 3 month intervals...so i think N would = 4? anyone confirm or deny?

mathslover · Answer

No : $$\large{A = 4000(1 + \frac{4.5}{5})^({4} \times 5)}$$ 
When we talk about counding quarterly than that means n would be 4

mathslover · Answer

^ $\large{4000 (1 + \frac{4.5}{4} )^{4\times 5}}$

anonymous · Answer

so it wouldnt be 4 quarters times 5 years, making it 20? it would just be 4?

johnweldon1993 · Answer

right....so

4000(1+(.045/4)) ^ (4 times 5)

mathslover · Answer

why 0.045 ?

anonymous · Answer

making it  adecimal, sine its a percent

anonymous · Answer

since*

mathslover · Answer

Oh I never did that.. I usually use this formula : 
$$\large{A = P (1+\frac{r}{100})^{nt} }$$ 
That's why I got confused :)

johnweldon1993 · Answer

right....yeah i usually use that as well @mathslover however i stayed in context for this one

johnweldon1993 · Answer

and it makes since too...if it WAS 4.5/4...that would be 1.125....that added to 1...would be 2.125....that a HUGE interest rate for a quarterly compound interest right?

mathslover · Answer

@zaynahf is ur doubt clear now?

mathslover · Answer

Yeah @johnweldon1993 :)

johnweldon1993 · Answer

it would make since that the interest for quarterly would be less than the annual compound

anonymous · Answer

Oh okay i see... well thanks! :)

mathslover · Answer

No problem. Though I didn't help :D

johnweldon1993 · Answer

You're welcome :)

johnweldon1993 · Answer

and @mathslover yeah you did...you both added context and confirmed....that's as helpful as anything in math lol

anonymous · Answer

Okay so would the answer be 5003.002?

johnweldon1993 · Answer

that's indeed what I get

anonymous · Answer

okay well thanks again

johnweldon1993 · Answer

no problem! :)