Question

The formula models​ inflation, where The value​ today, the annual inflation rate​ (in decimal​ form), and Stay inflated value t years from now. If the inflation rate is 6 ​%, how much will a house now worth ​$ 170000 be worth in 6​years? Round your answer to the nearest dollar.

Answer 1

Using the compound interest formula with an initial house value of $170,000 and a 6% annual inflation rate, the house will be approximately valued at $241,145 after 6 years.

Step-by-step explanation:

To calculate how much a house worth $170,000 will be worth in 6 years with an annual inflation rate of 6%, we apply the formula for compound interest, which is also used to calculate the value of an investment affected by inflation:
A = P(1 + r)^t

where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal).
• t is the time the money is invested for, in years.

Substituting the given values:
A = $170,000(1 + 0.06)^6

After calculating:
A = $170,000(1 + 0.06)^6
A = $170,000(1.4185)
A ≈ $241,145

Therefore, a house worth $170,000 today will be worth approximately $241,145 in 6 years considering a 6% annual inflation rate.