1. **State the problem:** Tom bought a stamp for 900 and it increases in value by 6.3% each year. We want to find the value after 18 years assuming geometric growth. 2. **Formula used:** The value after $t$ years with an annual increase rate $r$ is given by the compound interest formula: $$ V = P(1 + r)^t $$ where $P$ is the initial price, $r$ is the rate as a decimal, and $t$ is the time in years. 3. **Identify values:** - Initial price $P = 900$ - Rate $r = 6.3\% = 0.063$ - Time $t = 18$ years 4. **Calculate:** $$ V = 900(1 + 0.063)^{18} = 900(1.063)^{18} $$ 5. **Evaluate power:** $$ (1.063)^{18} \approx 3.054 $$ 6. **Multiply:** $$ V = 900 \times 3.054 = 2748.60 $$ 7. **Final answer:** The value of the stamp after 18 years is **2748.60**.