The formula [tex]S = C(1+r)^t[/tex] models inflation, where [tex]C[/tex] = the value today, [tex]r[/tex] = the annual inflation rate (in decimal form), and [tex]S[/tex] = the inflated value [tex]t[/tex] years from now. If the inflation rate is 5%, how much will a house now worth $66,000 be worth in 20 years? Round your answer to the nearest dollar.

The house will be worth $

Question

The house will be worth $

GinnyAnswer · Answer

Plug the given values into the inflation formula. 
 Calculate the value of ( 1.05 ) 20 . 
 Multiply the result by the current value of the house. 
 Round the final value to the nearest dollar: 175118 ​ . 
 
 Explanation 
 
 Understanding the Problem We are given the formula for inflation: S = C ( 1 + r ) t , where:

S is the inflated value after t years, 
 C is the current value, 
 r is the annual inflation rate (in decimal form), 
 t is the number of years. 
 
 We are given: 
 
 C = $66 , 000 (the current value of the house), 
 r = 5% = 0.05 (the annual inflation rate), 
 t = 20 years. 
 
 We want to find the value of the house in 20 years, which is S . 
 
 Substituting the Values Now, we substitute the given values into the formula: S = 66000 ( 1 + 0.05 ) 20 S = 66000 ( 1.05 ) 20 
 
 Calculating the Power We calculate ( 1.05 ) 20 :
 ( 1.05 ) 20 ≈ 2.653297705 
 
 Finding the Inflated Value Now, we multiply this by the current value of the house: S = 66000 × 2.653297705 ≈ 175117.6485 Rounding to the nearest dollar, we get S = $175 , 118 .

Examples 
 Understanding inflation is crucial in financial planning. For instance, if you plan to buy a house in the future, knowing how inflation affects property values helps you estimate the future cost and plan your savings accordingly. Similarly, businesses use inflation models to forecast future prices of goods and services, aiding in budgeting and investment decisions. This concept is also vital in understanding the real return on investments, as inflation erodes the purchasing power of money over time.

Anonymous · Answer

Using the inflation formula S = C ( 1 + r ) t , the house currently worth $66,000 will be worth approximately $175,118 in 20 years at an inflation rate of 5%. 
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