In the year 1985, a house was valued at 110,000 . By the...

In the year $1985,$ a house was valued at $\$ 110,000$ . By the year $2005,$ the value had appreciated to $\$ 145,000$ . What was the annual growth rate between 1985 and 2005$?$ Assume that the value continued to grow by the same percentage. What was the value of the house in the year 2010$?$

Key Concepts

Predictive Financial Modeling

Using the determined annual growth rate to forecast future values is a key aspect of predictive financial modeling. It involves applying the same compound interest formula to project the asset's value at a future time, assuming that the growth rate remains constant. This approach is widely used in finance and investment planning.

Compound Interest Formula

This formula, A = P(1 + r)^n, is used to calculate the future value of an investment or asset based on its initial value (P), an annual growth rate (r), and the number of compounding periods (n). It is fundamental in determining how an amount grows over time when the growth is compounded at regular intervals.

Exponential Growth

Exponential growth refers to the process in which an initial amount increases by a constant percentage over equal time periods. It is characterized by the multiplicative effect of growth, meaning that each period's growth builds upon the previous period's total, leading to faster increases over time.

Annual Growth Rate Calculation

Determining the annual growth rate involves solving the compound interest equation for the rate (r) given the initial value, the final value, and the number of years. This step is crucial in understanding how the value of an asset changes annually and forms the basis for predicting future values under consistent growth conditions.

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