In a suburb of Houston, housing costs have been increasing at 5.2% per a year compounded annually for the past 8 years. A house with a current value of $26,000 would have been worth how much 8 years ago?
Are you sure that's $26,000?
I bought a small inexpensive house in 1976 for $30,000. I sold it 14 years ago for $90,000.
I'm Sure.
To find out the value of the house 8 years ago, we can use the concept of compound interest.
Step 1: Convert the annual increase rate to a decimal form. The rate is given as 5.2%, so divide it by 100: 5.2% / 100 = 0.052.
Step 2: Use the compound interest formula: A = P(1 + r)^n, where:
- A is the final amount
- P is the initial amount (also known as the principal)
- r is the interest rate per period
- n is the number of periods
In this case, the initial amount (P) is $26,000, and the number of periods (n) is 8 years. We want to find out the value 8 years ago, so we need to solve for P.
Step 3: Rearrange the formula to solve for P:
P = A / (1 + r)^n
Now we can calculate the value of the house 8 years ago.
P = $26,000 / (1 + 0.052)^8
P = $26,000 / (1.052)^8
P ≈ $20,006.36
Therefore, a house with a current value of $26,000 would have been worth approximately $20,006.36 8 years ago in the suburb of Houston.