Question

kenny lives in greenpoint, where the cost of living increases by 8% every year. if kenny spends $50,700 this year, how much can he expect to spend 11 years from now to maintain the same standard of living? if necessary, round your answer to the nearest cent.

Explanation:

Step1: Identify the formula for compound growth

The formula for compound growth is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual growth rate (in decimal), and $t$ is the time in years.

Step2: Convert the percentage to decimal

The growth rate $r = 8\% = 0.08$.

Step3: Substitute the values into the formula

We have $P = 50700$, $r = 0.08$, and $t = 11$. So, $A = 50700(1 + 0.08)^{11}$.

Step4: Calculate $(1 + 0.08)^{11}$

First, calculate $1 + 0.08 = 1.08$. Then, $1.08^{11} \approx 2.331638945$.

Step5: Multiply by the principal amount

$A = 50700 \times 2.331638945 \approx 50700 \times 2.331638945 \approx 118214.00$.

Answer:

$\$118214.00$