Question

one account increased in value one year by 28% and decreased in value the next year by 28%. find and the \average rate\ of change for the account.
average rate = ______ % (hint: use a positive to represent an increase or a negative to represent a decrease. enter an integer or decimal number, accurate to at least 0 decimal places more..)

Explanation:

Step1: Assign initial account value

Let initial value be $V_0 = 100$ (any value works, 100 simplifies calculations).

Step2: Calculate year 1 value

Apply 28% increase:
$V_1 = V_0 \times (1 + 0.28) = 100 \times 1.28 = 128$

Step3: Calculate year 2 value

Apply 28% decrease to year 1 value:
$V_2 = V_1 \times (1 - 0.28) = 128 \times 0.72 = 92.16$

Step4: Compute total change over 2 years

Total change: $V_2 - V_0 = 92.16 - 100 = -7.84$

Step5: Find average annual rate

Let $r$ = average annual rate. Use total change over 2 years:
$100 \times (1 + r)^2 = 92.16$
$(1 + r)^2 = 0.9216$
$1 + r = \sqrt{0.9216} = 0.96$
$r = 0.96 - 1 = -0.04$
Convert to percentage: $r = -4\%$

Answer:

-4