Question

An amount of $10,000 is deposited in an account with an interest rate of r percent por year, compounded monthly. At the end of 3 years, the balance in the actount is given by A=10,000(1+ 1200r​ ) 36

(a) Find dr/dA​ , the rate of change of A with respect to r.
(b) Find dr/dA​ when r=3.6, and interpret the answer.

Answer 1

To find dr/dA, differentiate the equation A = 10,000(1 + 1200r)^36 using the chain rule. To find dr/dA when r = 3.6, substitute r = 3.6 into the equation for dr/dA.

Step-by-step explanation:

To find dr/dA, we need to differentiate the equation that relates A and r.

A = 10,000(1 + 1200r)^36

Using the chain rule, the derivative of A with respect to r is:

dr/dA = d/dA[10,000(1 + 1200r)^36]

To find dr/dA when r = 3.6, we can substitute r = 3.6 into the equation for dr/dA.

dr/dA = d/dA[10,000(1 + 1200(3.6))^36]