Question

An investment of P dollars made at the simple interest rate r for t years will grow to a total T = P + Prt. For an investment of 10,000 to grow to at least 12,000 in two years, what is the minimum interest rate at which it can be invested?

Answer 1

Hi! A lot of math speak in this one. Does it have you confused?

Answer 2

yea, sorry for bugging you though. It's from my math homework x__x

Answer 3

I got lost when it asked for the minimum rate

Answer 4

It's not a problem :)

Well, your total investment, \(T\), will be \(\sf \color{blue}{at\ least}\) \(12,000\). It can be \(12,000\) \(\sf\color{blue}{or\ greater}\). So, in math speak, \(T\ge12,000\).

Now, you want to solve for the interest rate, \(r\), and see what is the smallest value that you can have for it (that is the minimum).

Answer 5

ahh I see

Answer 6

:) So, are you ready to tackle the rest of the problem on your own? I'll still be here.

Answer 7

I'll try to

Answer 8

so the equation should start out like T = 10,000 + 12,000(r)2 right?

Answer 9

Close! You have \(P\) as 10,000 in one place and 12,000 in another!

Answer 10

I think that 12,000 should be a 10,000, since that's what \(P\) is. The 12,000 is \(T\).

Answer 11

oh yea

Answer 12

so now it's 12,000 = 10,000 + 2r?
just to be sure

Answer 13

12,000 = 10,000 + (10,000)2r :)

Answer 14

ahh ok thanks ^^

Answer 15

:)

Answer 16

alright thanks for the help ^^

Answer 17

You're welcome! Did you solve for \(r\)?

Answer 18

yea , but I'm kind of unsure of it though ^^|| I got 0.1 = r. I'm sure if I got it right or not

Answer 19

~not sure~

Answer 20

Yeah! \(.1\ge r\), so the smallest \(r\), a.k.a. the "minimum interest rate," is \(.1\). Sometimes rates are percentages, so you might want to say \(.1=10\%=r_\text{minimum}\)

Answer 21

So I agree with you!:)

Answer 22

oh ok thank you :3

Answer 23

No problem.