QuestionSelect the correct interpretation of $10,785(1.0275)^{x}$ for an investment with annual compounding interest.

Studdy Solution

STEP 1

Assumptions1. The expression $10,785(1.0275)^{x}$ represents the amount of money in an investment account with interest that compounds annually for $x$ years. . The number $10,785$ represents the initial investment.
3. The number $1.0275$ represents the growth rate of the investment plus1.
4. The variable $x$ represents the number of years the money is invested.

STEP 2

We can interpret the expression by understanding what each part of the expression represents. The initial investment is represented by the number $10,785$ .

STEP 3

The growth rate of the investment is represented by the number $1.0275$ . However, this number includes the initial amount of the investment (represented by1) plus the growth rate. Therefore, to find the growth rate, we need to subtract1 from $1.0275$ .
$Growth\, rate =1.0275 -1$

STEP 4

Calculate the growth rate.
$Growth\, rate =1.027 -1 =0.027$

STEP 5

The growth rate is usually expressed as a percentage. To convert the growth rate to a percentage, we multiply by100.
$Growth\, rate\, (\%) =0.0275 \\times100$

STEP 6

Calculate the growth rate in percentage.
$Growth\, rate\, (\%) =0.0275 \\times100 =2.75\%$ The initial investment is $\$10,785$ , and the growth rate of the investment is $2.75 \%$ .
Therefore, the correct answer is. The initial investment is $\$10,785$ , and the growth rate of the investment is $2.75 \%$ .

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