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15,000 loses value by 20% each year. What is the value after 3 years

2 Answers

4 votes
So you have 15,000, which decreases in value by 20% each year. The question asks, what is the value after 3 years. So you would have 15,000(1-0.2)^3 and that is your equation. The reason for this is because you have your initial value 15,000, and when it is a percent decrease, you use the formula i(1-d)^x, where i represents the initial value, d represents the percent decrease, and x represents the number of years. We can convert 20% into a decimal as 0.2. So our initial value is 15000, our percent decrease is 0.2, and number of years we can see is 3. That is why the equation is 15,000(1-0.2)^3. I would solve this using PEMDAS, meaning that Parenthesis comes first, Exponents come second, and then Multiplication comes after both of those. I stopped here because these are the only three things we need to do to solve. When I solve this, I do (1-0.2) = 0.8, and (0.8)^3 = 0.512. Then I multiply 15,000 with 0.512, which gives me 7680. Therefore the value of 15000 after 3 years is $7680. Hope this helps. Feel free to ask me questions about my explanation, and feel free to post more questions.
User Karthik Malla
by
7.0k points
3 votes

Answer:

Step-by-step explanation: 7680

After losing 20% we have 80% remaining

∴ value after three years = 15,000 ×
(80)/(100) ×
(80)/(100) ×
(80)/(100)

= 15,000 ×
(4)/(5) ×
(4)/(5) ×
(4)/(5)

= 7680

User Kuldip Saini
by
6.8k points