Question

An heirloom necklace is priced at $830 and gains value at a rate of 2.5% each year how much will it be worth in 10 years?

Answer 1

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.

`(2.5)/(100)=0.025`

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

`100\%=1\Rightarrow100\%+2.5\%=1+0.025=1.025`

then, the value after one year is given by

`830\cdot1.025`

and every year that passes, we multiply by this factor

`830\cdot1.025\cdot1.025...\cdot1.025=830\cdot1.025^n`

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

`830\cdot1.025^(10)=1062.47017168...\approx1062.47`

The price after 10 years will be $1062.47.