Each year the necklace gains 2.5% of its own value. To write a percentage as a decimal number, we just divide it by 100.
[tex]\frac{2.5}{100}=0.025[/tex]Since each year the necklace gains 2.5% of its own value, this means that each year we multiply the previous price by 100% plus this rate, which is
[tex]100\%=1\Rightarrow100\%+2.5\%=1+0.025=1.025[/tex]then, the value after one year is given by
[tex]830\cdot1.025[/tex]and every year that passes, we multiply by this factor
[tex]830\cdot1.025\cdot1.025...\cdot1.025=830\cdot1.025^n[/tex]The amount of times we multiply, is the amount of years that passed. Since we want to know the price after 10 years, the calculation is
[tex]830\cdot1.025^{10}=1062.47017168...\approx1062.47[/tex]The price after 10 years will be $1062.47.
