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

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

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

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

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

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

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

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

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

I've got $\displaystyle r \approx 0.08321$