Question

If 1200 dollars is invested at an annual interest rate r compounded monthly, the amount in the account at the end of 3 years is given by A = 1200 ( 1 + 1 12 r ) 36 . Find the rate of change of the amount A with respect to the rate r for the following values of r :

Answer 1

Answer:

a. When r = 4 percent, the rate of change is 22.10%.

b. When r = 7 percent, the rate of change is 41.76%.

Explanation:

Note: This question is not complete the required values of r is omitted. To complete the question, these values are therefore provided before answering the question as follows:

Find the rate of change of the amount A with respect to the rate r for the following values of r:

a. r = 4 percent

b. r = 7 percent

The explanation of the answer is now given as follows:

The A given is correctly stated as follows:

A = 1200 * (1 + ((1/12) * r))^60 ……………………….. (1)

Therefore, we have:

a. When r = 4 percent

Substituting r = 4% into equation (1), we have:

A = 1200 * (1 + ((1/12) * 4%))^60 = 1200 * 1.22099659394212 = 1465.20

Rate of change = (A - Amount invested) / Amount invested = (1465.20 - 1200) / 1200 = 0.2210, or 22.10%

Therefore, when r = 4 percent, the rate of change is 22.10%.

b. When r = 7 percent

Substituting r = 7% into equation (1), we have:

A = 1200 * (1 + ((1/12) * 7%))^60 = 1200 * 1.41762525961399 = 1701.15

Rate of change = (A - Amount invested) / Amount invested = (1701.15 - 1200) / 1200 = 0.4176, or 41.76%

Therefore, when r = 7 percent, the rate of change is 41.76%.