Expert: Paul Klarreich - 2/25/2007

Question
i need help in my calculus homework...this is one of the problems:

*if $1000 is invested at interest rate i, compounded annually, it will grow in 3 years to an amount A given by A=1000(1+i)^3. Find the rate of change, dA/di.

thanks!

Answer
Questioner:   meg
Category:  Calculus
 
Subject:  related rates << Not really.
Question:  I need help in my calculus homework...this is one of the problems:

*if $1000 is invested at interest rate r, compounded annually, it will grow in 3 years to an amount A given by A=1000(1+r)^3. Find the rate of change, dA/dr.

thanks!
...................................
Hi, Meg,

[I changed the 'i' to an 'r', for RRRRRate.]

If this is all you need, it's just a Chain Rule example:

A = 1000 (1 + r)^3

Let u = 1 + r,  du/dr = 1
Then A = 1000 u^3,  dA/du = 3000 u^2

Finally,
dA   dA du
-- = -- -- = 3000(1 + r)^2(1) = 3000(1 + r)^2
dr   du dr