Ask a New Question
Menu

Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 1 to 4 by increments of 1 and is labeled Time with decade as the units. The y-axis ranges from 0 to 10,000 by increments of 1,000 and is labeled Current Balance with dollar as the units. A solid curve is plotted.

The graph shows the total amount of an investment account with a principal of $1,500 which increases 1.5 times every 10 years. Use the graph to estimate the total amount of the account if $1,500 is invested for 32 years.

(1 point)
Responses

$7,800
$7,800

$5,500
$5,500

$5,000
$5,000

$6,200

1 answer

To estimate the total amount of the account after 32 years, we can analyze the growth pattern given in the problem. The investment increases by a factor of 1.5 every 10 years.

Here's how to calculate it:

  1. First, determine how many 10-year periods are in 32 years: \[ 32 \text{ years} \div 10 \text{ years/period} = 3.2 \text{ periods} \] This means there are 3 full periods of 10 years, and a fraction of a period (0.2 of a period).

  2. Next, calculate the amount after the full 10-year periods:

    • After the first 10 years: \[ 1500 \times 1.5 = 2250 \]
    • After the second 10 years: \[ 2250 \times 1.5 = 3375 \]
    • After the third 10 years: \[ 3375 \times 1.5 = 5062.5 \]

  3. Now, account for the additional 0.2 of a period (or 2 years out of 10): Since the investment typically increases by a factor of 1.5 every 10 years, we can find 2 years' worth of growth: \[ 1.5^{(2/10)} \approx 1.5^{0.2} \approx 1.1147 \] (You can use a scientific calculator or estimation to find this growth factor).

  4. Now, multiply the amount after 30 years by the growth factor for the additional 2 years: \[ 5062.5 \times 1.1147 \approx 5655.38 \]

Given the options provided, the closest amount is:

  • $5,500

Therefore, the estimated total amount of the account if $1,500 is invested for 32 years is approximately $5,500.