Math / Algebra

QuestionFinding a final amount in a word problem on exponential growth or decay
A principal of $\$ 4400$ is invested at $8.5 \%$ interest, compounded annually. How much will the investment be worth after 8 years? Use the calculator provided and round your answer to the nearest dollar. $\square$

Studdy Solution

STEP 1

What is this asking? How much money will we have if we put $\$4400$ in a savings account with an interest rate of $8.5\%$ compounded annually for 8 years? Watch out! Don't forget to convert the percentage to a decimal!

STEP 2

1. Define the formula
2. Calculate the growth factor
3. Calculate the final amount

STEP 3

We can use the formula for compound interest: $A = P(1 + r)^t$ Where: $A$ is the future value of the investment/loan, including interest. $P$ is the principal amount ( $\$4400$ in our case - the initial amount we're starting with). $r$ is the annual interest rate (decimal). $t$ is the time the money is invested or borrowed for in years.

STEP 4

Let's convert our interest rate to a decimal. $8.5\%$ is the same as $\frac{8.5}{100}$ , which equals $0.085$ .
This is our r value.

STEP 5

Now, let's calculate the growth factor, which is $(1 + r)$ . $1 + r = 1 + 0.085 = 1.085$ This means our investment grows by a factor of 1.085 each year!

STEP 6

Let's plug in our values into the formula: $A = P(1 + r)^t$ $A = 4400 \cdot (1.085)^8$

STEP 7

Now, let's calculate $(1.085)^8$ : $(1.085)^8 \approx 1.920500$

STEP 8

Finally, let's multiply this by our principal amount: $A = 4400 \cdot 1.920500$ $A \approx 8450.20$

STEP 9

After 8 years, the investment will be worth approximately $\$8450$ .

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QuestionFinding a final amount in a word problem on exponential growth or decay
A principal of $\$ 4400$ is invested at $8.5 \%$ interest, compounded annually. How much will the investment be worth after 8 years? Use the calculator provided and round your answer to the nearest dollar. $\square$

Studdy Solution

STEP 1

What is this asking? How much money will we have if we put $\$4400$ in a savings account with an interest rate of $8.5\%$ compounded annually for 8 years? Watch out! Don't forget to convert the percentage to a decimal!

STEP 2

1. Define the formula
2. Calculate the growth factor
3. Calculate the final amount

STEP 3

STEP 4

Let's convert our interest rate to a decimal. $8.5\%$ is the same as $\frac{8.5}{100}$ , which equals $0.085$ .
This is our r value.

STEP 5

Now, let's calculate the growth factor, which is $(1 + r)$ . $1 + r = 1 + 0.085 = 1.085$ This means our investment grows by a factor of 1.085 each year!

STEP 6

Let's plug in our values into the formula: $A = P(1 + r)^t$ $A = 4400 \cdot (1.085)^8$

STEP 7

Now, let's calculate $(1.085)^8$ : $(1.085)^8 \approx 1.920500$

STEP 8

Finally, let's multiply this by our principal amount: $A = 4400 \cdot 1.920500$ $A \approx 8450.20$

STEP 9

After 8 years, the investment will be worth approximately $\$8450$ .

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Studdy Solution

STEP 1

What is this asking? How much money will we have if we put $4400\$4400$4400 in a savings account with an interest rate of 8.5%8.5\%8.5% compounded annually for 8 years? Watch out! Don't forget to convert the percentage to a decimal!

STEP 2

1. Define the formula2. Calculate the growth factor3. Calculate the final amount

STEP 3

STEP 4

Let's **convert** our interest rate to a decimal. 8.5%8.5\%8.5% is the same as 8.5100\frac{8.5}{100}1008.5​, which equals 0.0850.0850.085.This is our **r** value.

STEP 5

Now, let's calculate the **growth factor**, which is (1+r)(1 + r)(1+r). 1+r=1+0.085=1.085 1 + r = 1 + 0.085 = 1.085 1+r=1+0.085=1.085 This means our investment grows by a factor of **1.085** each year!

STEP 6

Let's **plug in** our values into the formula: A=P(1+r)t A = P(1 + r)^t A=P(1+r)t A=4400⋅(1.085)8 A = 4400 \cdot (1.085)^8 A=4400⋅(1.085)8

STEP 7

Now, let's **calculate** (1.085)8(1.085)^8(1.085)8: (1.085)8≈1.920500 (1.085)^8 \approx 1.920500 (1.085)8≈1.920500

STEP 8

Finally, let's **multiply** this by our **principal amount**: A=4400⋅1.920500 A = 4400 \cdot 1.920500 A=4400⋅1.920500 A≈8450.20 A \approx 8450.20 A≈8450.20

STEP 9

After 8 years, the investment will be worth approximately $8450\$8450$8450.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? How much money will we have if we put $\$4400$ in a savings account with an interest rate of $8.5\%$ compounded annually for 8 years? Watch out! Don't forget to convert the percentage to a decimal!

1. Define the formula
2. Calculate the growth factor
3. Calculate the final amount

Let's convert our interest rate to a decimal. $8.5\%$ is the same as $\frac{8.5}{100}$ , which equals $0.085$ .
This is our r value.

Now, let's calculate the growth factor, which is $(1 + r)$ . $1 + r = 1 + 0.085 = 1.085$ This means our investment grows by a factor of 1.085 each year!

Let's plug in our values into the formula: $A = P(1 + r)^t$ $A = 4400 \cdot (1.085)^8$

Now, let's calculate $(1.085)^8$ : $(1.085)^8 \approx 1.920500$

Finally, let's multiply this by our principal amount: $A = 4400 \cdot 1.920500$ $A \approx 8450.20$

After 8 years, the investment will be worth approximately $\$8450$ .