Math / Algebra

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The principal $P$ is borrowed at simple interest rate $r$ for a period of time $t$ . Find the loan's future value, $A$ , or the total amount due at time t. $P=\$ 9000, r=6.5 \%, t=8 \text { months }$
The future value is $\$$ $\square$ (Simplify your answer. Type an integer or a decimal.)

Studdy Solution

STEP 1

What is this asking? We need to find the total amount due on a loan of $\$9000$ after 8 months at a simple interest rate of $6.5\%$ . Watch out! The time is given in months, but the interest rate is annual.
We need to convert the time to years!

STEP 2

1. Convert time to years
2. Calculate the interest
3. Calculate the future value

STEP 3

Since there are 12 months in a year, we can convert 8 months to years by dividing by 12: $t = \frac{8 \text{ months}}{12 \text{ months/year}} = \frac{8}{12} \text{ years} = \frac{2}{3} \text{ years}$ So, the time is $\frac{2}{3}$ of a year.

STEP 4

The simple interest formula is given by: $I = P \cdot r \cdot t$ Where $I$ is the interest, $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in years.

STEP 5

We know that $P = \$9000$ , $r = 6.5\% = 0.065$ , and $t = \frac{2}{3}$ years.
Let's plug these values into the formula: $I = \$9000 \cdot 0.065 \cdot \frac{2}{3}$

STEP 6

Now, let's calculate the interest: $I = \$9000 \cdot 0.065 \cdot \frac{2}{3} = \$585 \cdot \frac{2}{3} = \$390$ So, the interest earned is $\$390$ .

STEP 7

The future value, $A$ , is the sum of the principal and the interest: $A = P + I$

STEP 8

We know that $P = \$9000$ and $I = \$390$ , so: $A = \$9000 + \$390 = \$9390$

STEP 9

The future value of the loan is $\$9390$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the total amount due on a loan of $\$9000$ after 8 months at a simple interest rate of $6.5\%$ . Watch out! The time is given in months, but the interest rate is annual.
We need to convert the time to years!

STEP 2

1. Convert time to years
2. Calculate the interest
3. Calculate the future value

STEP 3

Since there are 12 months in a year, we can convert 8 months to years by dividing by 12: $t = \frac{8 \text{ months}}{12 \text{ months/year}} = \frac{8}{12} \text{ years} = \frac{2}{3} \text{ years}$ So, the time is $\frac{2}{3}$ of a year.

STEP 4

The simple interest formula is given by: $I = P \cdot r \cdot t$ Where $I$ is the interest, $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in years.

STEP 5

We know that $P = \$9000$ , $r = 6.5\% = 0.065$ , and $t = \frac{2}{3}$ years.
Let's plug these values into the formula: $I = \$9000 \cdot 0.065 \cdot \frac{2}{3}$

STEP 6

Now, let's calculate the interest: $I = \$9000 \cdot 0.065 \cdot \frac{2}{3} = \$585 \cdot \frac{2}{3} = \$390$ So, the interest earned is $\$390$ .

STEP 7

The future value, $A$ , is the sum of the principal and the interest: $A = P + I$

STEP 8

We know that $P = \$9000$ and $I = \$390$ , so: $A = \$9000 + \$390 = \$9390$

STEP 9

The future value of the loan is $\$9390$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the total amount due on a loan of $9000\$9000$9000 after 8 months at a simple interest rate of 6.5%6.5\%6.5%. Watch out! The time is given in months, but the interest rate is annual.We need to convert the time to years!

STEP 2

1. Convert time to years2. Calculate the interest3. Calculate the future value

STEP 3

STEP 4

The simple interest formula is given by: I=P⋅r⋅t I = P \cdot r \cdot t I=P⋅r⋅t Where III is the **interest**, PPP is the **principal**, rrr is the **annual interest rate**, and ttt is the **time in years**.

STEP 5

We know that P=$9000P = \$9000P=$9000, r=6.5%=0.065r = 6.5\% = 0.065r=6.5%=0.065, and t=23t = \frac{2}{3}t=32​ years.Let's plug these values into the formula: I=$9000⋅0.065⋅23 I = \$9000 \cdot 0.065 \cdot \frac{2}{3} I=$9000⋅0.065⋅32​

STEP 6

Now, let's calculate the interest: I=$9000⋅0.065⋅23=$585⋅23=$390 I = \$9000 \cdot 0.065 \cdot \frac{2}{3} = \$585 \cdot \frac{2}{3} = \$390 I=$9000⋅0.065⋅32​=$585⋅32​=$390 So, the interest earned is $390\$390$390.

STEP 7

The future value, AAA, is the sum of the **principal** and the **interest**: A=P+I A = P + I A=P+I

STEP 8

We know that P=$9000P = \$9000P=$9000 and I=$390I = \$390I=$390, so: A=$9000+$390=$9390 A = \$9000 + \$390 = \$9390 A=$9000+$390=$9390

STEP 9

The future value of the loan is $9390\$9390$9390.

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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? We need to find the total amount due on a loan of $\$9000$ after 8 months at a simple interest rate of $6.5\%$ . Watch out! The time is given in months, but the interest rate is annual.
We need to convert the time to years!

1. Convert time to years
2. Calculate the interest
3. Calculate the future value

The simple interest formula is given by: $I = P \cdot r \cdot t$ Where $I$ is the interest, $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in years.

We know that $P = \$9000$ , $r = 6.5\% = 0.065$ , and $t = \frac{2}{3}$ years.
Let's plug these values into the formula: $I = \$9000 \cdot 0.065 \cdot \frac{2}{3}$

Now, let's calculate the interest: $I = \$9000 \cdot 0.065 \cdot \frac{2}{3} = \$585 \cdot \frac{2}{3} = \$390$ So, the interest earned is $\$390$ .

The future value, $A$ , is the sum of the principal and the interest: $A = P + I$

We know that $P = \$9000$ and $I = \$390$ , so: $A = \$9000 + \$390 = \$9390$

The future value of the loan is $\$9390$ .