Problem 66 - College Algebra

Question

The formula \(S-C(1+r)^{t}\) models inflation, where \(C\) - the value today, \(r-\) the annual inflation rate, and \(S\) - the inflated value \(t\) years from now. Use this formula to solve Exercises \(67-68\). Round answers to the nearest dollar. If the inflation rate is \(6 \%,\) how much will a house now worth \(\$ 465,000\) be worth in 10 years?

Step-by-Step Solution

Answer

The inflated value of the house in 10 years assuming an inflation rate of 6% will be \$826,344

Step 1: Convert Percentage to Decimal

The annual inflation rate is given as \(6\% \). Convert this percentage to a decimal by dividing by 100. Hence, \(r = 6\% = 0.06\)

Step 2: Substitute into the Inflation Formula

Substitute the given values into the inflation model function \(S = C(1+r)^t\). Hence, \(S = \$465,000 (1+0.06)^{10}\)

Step 3: Calculate the inflated value

Perform the calculations to get the inflated value. \(S = \$465,000(1.06)^{10}\) is approximately \$826,343.94

Step 4: Round off the answer

Now round off this value to the nearest dollar to get \$826,344