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Compound interest is a concept in finance where interest earned over time is added to the principal amount. This means you earn interest on your initial investment as well as on the interest accumulated. It's the key to understanding how investments grow exponentially over time.
The compound interest formula is: A = P (1 + r)^t, where:

- P = principal amount (initial investment) - r = annual interest rate (expressed as a decimal)
- t = time the money is invested for (in years) - A = amount of money accumulated after n years, including interest

. This formula helps calculate the future value of an investment, taking into account the effect of compound interest.

Price appreciation refers to the increase in the value of an asset over time. In the context of real estate, it indicates the rise in the price of a property due to various factors like demand, market trends, and economic conditions. For a condominium initially priced at $$ 90,000\(, we need to account for a 3 %\) annual appreciation rate. This involves calculating how the value appreciates each year and combining these increases over the given period. Compounding plays a crucial role here, as each year's appreciation builds upon the previous year's increased value.

The future value calculation helps determine the worth of an investment or asset at a specific point in the future. Using the compound interest formula, substituting the known values: initial price ($$ 90,000\(), annual appreciation rate (3 %, as a decimal 0.03\)) and time frame (5\( years), we proceed:
Plug these into A = P(1 + r)^t\): A = 90,000 (1 + 0.03)^5\(. Calculating inside the parenthesis: (1 + 0.03) = 1.03\). Raising this to the power of 5\(: 1.03^5 = 1.159274\). Finally, multiplying the initial investment by this compound factor gives: 90,000 \times 1.159274 = 104,334.66\(. Therefore, after 5\) years, the condominium will cost approximately 104,334.66$. This calculation demonstrates the power of compounding and how it impacts price appreciation for investments over time.