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QuestionKenny's spending increases by 8%8\% annually. If he spends \$50,700 now, what will he spend in 11 years?

Studdy Solution

STEP 1

Assumptions1. The current cost of living for Kenny is $50,700. The cost of living increases by8% every year3. We want to find out the cost of living11 years from now

STEP 2

We can model the increase in cost of living as an exponential growth problem. The formula for exponential growth isFuture value=Present valuetimes(1+Growth rate)Number of periodsFuture\, value = Present\, value \\times (1 + Growth\, rate)^{Number\, of\, periods}

STEP 3

Now, plug in the given values for the present value, growth rate, and number of periods to calculate the future value.
Future value=$50,700times(1+8%)11Future\, value = \$50,700 \\times (1 +8\%)^{11}

STEP 4

Convert the percentage to a decimal value.
8%=0.088\% =0.08Future value=$50,700times(1+0.08)11Future\, value = \$50,700 \\times (1 +0.08)^{11}

STEP 5

Calculate the future value.
Future value=$50,700times(1.08)11Future\, value = \$50,700 \\times (1.08)^{11}

STEP 6

Using a calculator, we find that the future value is approximately \$116,283.22Kenny can expect to spend approximately \$116,283.22,11 years from now to maintain the same standard of living.

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