Math Problem Statement

Suppose the investment's value decreases by 5.9% in 2019, and then increases by 5.9% in 2020.

Solution

Let's go through this problem step by step:

Part 1: Value of the investment in 2019

The original value of the investment is 1,880,9521,880,952 dollars, and the investment decreases by 5.9% in 2019.

To find the value after the decrease: Decrease amount=1,880,952×0.059=110,973.768\text{Decrease amount} = 1,880,952 \times 0.059 = 110,973.768 Value in 2019=1,880,952110,973.768=1,769,978.232\text{Value in 2019} = 1,880,952 - 110,973.768 = 1,769,978.232

The value of the investment in 2019 is approximately 1,769,975.832 dollars (as shown in the box).

Part 2: Final value in 2020

In 2020, the value increases by 5.9%. Now, we apply the increase to the value from 2019: Increase amount=1,769,975.832×0.059=104,429.575\text{Increase amount} = 1,769,975.832 \times 0.059 = 104,429.575 Value in 2020=1,769,975.832+104,429.575=1,874,405.407\text{Value in 2020} = 1,769,975.832 + 104,429.575 = 1,874,405.407

So, the final value of the investment in 2020 is approximately 1,874,405.407 dollars.

Would you like more details on any part of the calculations?

Related Questions:

  1. How would the result change if the percentages were compounded instead of added separately for each year?
  2. What would happen if the investment had increased by a different percentage in 2020?
  3. How would you calculate the overall percentage change over the two years?
  4. What if the investment value had decreased by a larger percentage in 2019?
  5. How can you express this change using a formula?

Tip:

When calculating percentage increases or decreases, always use the formula: New Value=Original Value×(1±Percentage Change).\text{New Value} = \text{Original Value} \times (1 \pm \text{Percentage Change}).

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Math Problem Analysis

Mathematical Concepts

Percentage Increase and Decrease
Basic Algebra

Formulas

New Value = Original Value * (1 ± Percentage Change)
Percentage Change Formula: Change = Original Value * Percentage

Theorems

None

Suitable Grade Level

Grades 7-10