# Rate of Change

• Mar 27th 2009, 11:14 AM
magentarita
Rate of Change
Suppose a sum of $500 is deposited in an account with an interest rate of r percent per year compounded monthly. At the end of 10 years, the balance in the account is given by: A = 500(1+r/1200)^(120) Find the rate of change of A with respect to r if r = 5 Do I solve the above equation for A given that r = 5? • Mar 27th 2009, 11:57 AM TheEmptySet Quote: Originally Posted by magentarita Suppose a sum of$500 is deposited in an account with an interest rate of r percent per year compounded monthly. At the end of 10 years, the balance in the account is given by:

A = 500(1+r/1200)^(120)

Find the rate of change of A with respect to r if r = 5

Do I solve the above equation for A given that r = 5?

The rate of change means the slope or the value of the derivative at the point in question.

Since this is in the pre-calc section I am not sure if you know how to take derivatives. Otherwise it could be estimated by using secant lines.

Let us know which method you are supposed to use.

Good luck. (Rock)
• Mar 27th 2009, 05:16 PM
magentarita
take derivatives
Quote:

Originally Posted by TheEmptySet
The rate of change means the slope or the value of the derivative at the point in question.

Since this is in the pre-calc section I am not sure if you know how to take derivatives. Otherwise it could be estimated by using secant lines.

Let us know which method you are supposed to use.

Good luck. (Rock)

I have to take the derivative. Can you show me how to do that?
• Mar 27th 2009, 08:13 PM
TheEmptySet
Quote:

Originally Posted by magentarita
Suppose a sum of \$500 is deposited in an account with an interest rate of r percent per year compounded monthly. At the end of 10 years, the balance in the account is given by:

A = 500(1+r/1200)^(120)

Find the rate of change of A with respect to r if r = 5

Do I solve the above equation for A given that r = 5?

We need to use the chain rule

$\frac{dA}{dr}=500\cdot 120\left( 1+\frac{r}{1200}\right)^{119}\cdot \left( \frac{1}{1200}\right)=50\left(1+\frac{r}{1200} \right)^{119}$

From here just evaluate at r=5 and you are done. :)