# interest rates.

• Feb 22nd 2011, 08:39 AM
candisweet
interest rates.
I'm not sure if this belongs here or not- I am taking a contemporary mathematics course this semester and I missed a day of class. The name of the title is Finding interest rates.

I already have the anwser, just need someone's help explaining how to solve the problem.
For example: Suppose you invest $10,000 on your son's 13th birthday and it accumulates to 15,000 on his 18th birthday. What annual rate of compound interest did this investment earn? Pv=10,000 fv=15,000 t=5 years answer 8.45% Please help me. • Feb 22nd 2011, 09:18 AM e^(i*pi) The compound interest formula is$\displaystyle F_v = P_v \left(1 + \dfrac{r}{n}\right)^{nt}$where •$\displaystyle F_v $= Final Value •$\displaystyle P_v$= Initial Value •$\displaystyle r$= Annualised interest rate •$\displaystyle n$= number of compounds per year •$\displaystyle t$= number of years You know$\displaystyle F_v = 15000$,$\displaystyle P_v = 10000$,$\displaystyle n = 1$(it's compounded annually) and$\displaystyle t = 5$Plug and Chug gives:$\displaystyle r = \sqrt[5]{\dfrac{F_v}{P_v}} - 1$• Feb 22nd 2011, 09:22 AM TheEmptySet Quote: Originally Posted by candisweet I'm not sure if this belongs here or not- I am taking a contemporary mathematics course this semester and I missed a day of class. The name of the title is Finding interest rates. I already have the anwser, just need someone's help explaining how to solve the problem. For example: Suppose you invest$10,000 on your son's 13th birthday and it accumulates to 15,000 on his 18th birthday. What annual rate of compound interest did this investment earn?

Pv=10,000 fv=15,000 t=5 years answer 8.45%

Well the compound interest formula is

$\displaystyle \displaystyle P=P_0\left(1+\frac{r}{n}\right)^{nt}$

and you are given $\displaystyle P=15000,P_0=100000,n=1,t=5$
Putting all of this into the equation gives

$\displaystyle \displaystyle 15000=10000\left(1+r\right)^{5}$

Can you finish from here?

Edit: too slow
• Feb 22nd 2011, 10:56 AM
candisweet
I know how to set the initial problem, but I guess what I'm asking is for the detailed steps because I cant figure it out, like how to isolate r, I think. Im so confused. Sorry math is not my thing.

I get to here.

15,000=10,000(1 + r) 5
(15,000 /10,000 -1) = r 5
don't know how to go further.
• Feb 22nd 2011, 11:09 AM
e^(i*pi)
You have (1+r)^5 which is definitely not "r 5"

I have solved the equation for r in post 2 (but note that you take the 5th root before subtracting 1)

If your calculator does not have a 5th root button raise it to the power of 0.2
• Feb 22nd 2011, 11:15 AM
candisweet
Thanks. I wasn't using my calculator right. I got the answer! thanks so much
• Feb 22nd 2011, 12:47 PM
Wilmer
REMEMBER: if a^p = b, then a = b^(1/p) ; TATTOO that on your wrist !