# find the rate, solve for r

• Dec 8th 2011, 07:54 PM
delgeezee
find the rate, solve for r
I ussually dont need help for the types of question, but I am having alot of diffuculty isolating r by itself on one side of the = sign.

Assume a person invests $210 at the end of each year for 10 years at an annual interest rate of r. The ammount of money, A, in the account after 10 years is A = $\frac{210((1+r)^{10}-1)}{r}$ his goal is to have 3089 in his account after 10 years. $\frac{210((1+r)^{10}-1)}{r}= 3089$ • Dec 8th 2011, 10:16 PM earboth Re: find the rate, solve for r Quote: Originally Posted by delgeezee I ussually dont need help for the types of question, but I am having alot of diffuculty isolating r by itself on one side of the = sign. Assume a person invests$210 at the end of each year for 10 years at an annual interest rate of r. The ammount of money, A, in the account after 10 years is
A = $\frac{210((1+r)^{10}-1)}{r}$

his goal is to have 3089 in his account after 10 years.

$\frac{210((1+r)^{10}-1)}{r}= 3089$

This is an equation of 9th degree in r. I doubt that you'll find a solution in closed form.

Re-arrange the equation to

$(1+r)^{10}-\frac{3089}{210} r -1 =0$

and use (for instance) Newton's method to get an approximate value of r.

I've got $r \approx 0.08321$