Math / Algebra

QuestionJamal wants to save $\$ 59,000$ for a down payment on a home. How much will he need to invest in an account with 9\% APR, compounding daily, in order to reach his goal in 7 years? Round to the nearest dollar.
He will need to invest \\square$
Question Help: Written Example

Studdy Solution

STEP 1

1. Jamal wants to save $59,000 for a down payment.
2. The account has an annual percentage rate (APR) of 9%.
3. The interest is compounded daily.
4. The investment period is 7 years.
5. We need to find the present value (initial investment) required to reach the goal.

STEP 2

1. Understand the formula for compound interest.
2. Identify the variables in the formula.
3. Substitute the known values into the formula.
4. Solve for the present value.
5. Round the result to the nearest dollar.

STEP 3

Understand the formula for compound interest. The formula for compound interest when compounding daily is:
$A = P \left(1 + \frac{r}{n}\right)^{nt}$
where: - $A$ is the amount of money accumulated after n years, including interest. - $P$ is the principal amount (the initial amount of money). - $r$ is the annual interest rate (decimal). - $n$ is the number of times that interest is compounded per year. - $t$ is the time the money is invested for in years.

STEP 4

Identify the variables in the formula.
- $A = 59,000$ (the future value Jamal wants) - $r = 0.09$ (9% annual interest rate) - $n = 365$ (compounded daily) - $t = 7$ (years)

STEP 5

Substitute the known values into the formula:
$59,000 = P \left(1 + \frac{0.09}{365}\right)^{365 \times 7}$

STEP 6

Solve for the present value $P$ .
First, calculate the expression inside the parentheses:
$1 + \frac{0.09}{365} \approx 1.0002465753$
Next, calculate the exponent:
$365 \times 7 = 2555$
Now, calculate the entire expression:
$\left(1.0002465753\right)^{2555} \approx 1.883679918$
Substitute back to solve for $P$ :
$59,000 = P \times 1.883679918$
$P = \frac{59,000}{1.883679918}$
$P \approx 31,312.68$

STEP 7

Round the result to the nearest dollar.
$P \approx 31,313$
Jamal will need to invest \$31,313.

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QuestionJamal wants to save $\$ 59,000$ for a down payment on a home. How much will he need to invest in an account with 9\% APR, compounding daily, in order to reach his goal in 7 years? Round to the nearest dollar.
He will need to invest \\square$
Question Help: Written Example

Studdy Solution

STEP 1

1. Jamal wants to save $59,000 for a down payment.
2. The account has an annual percentage rate (APR) of 9%.
3. The interest is compounded daily.
4. The investment period is 7 years.
5. We need to find the present value (initial investment) required to reach the goal.

STEP 2

1. Understand the formula for compound interest.
2. Identify the variables in the formula.
3. Substitute the known values into the formula.
4. Solve for the present value.
5. Round the result to the nearest dollar.

STEP 3

STEP 4

Identify the variables in the formula.
- $A = 59,000$ (the future value Jamal wants) - $r = 0.09$ (9% annual interest rate) - $n = 365$ (compounded daily) - $t = 7$ (years)

STEP 5

Substitute the known values into the formula:
$59,000 = P \left(1 + \frac{0.09}{365}\right)^{365 \times 7}$

STEP 6

STEP 7

Round the result to the nearest dollar.
$P \approx 31,313$
Jamal will need to invest \$31,313.

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QuestionJamal wants to save $59,000\$ 59,000$59,000 for a down payment on a home. How much will he need to invest in an account with 9\% APR, compounding daily, in order to reach his goal in 7 years? Round to the nearest dollar.He will need to invest \ \square$Question Help: Written Example

Studdy Solution

STEP 1

1. Jamal wants to save $59,000 for a down payment.2. The account has an annual percentage rate (APR) of 9%.3. The interest is compounded daily.4. The investment period is 7 years.5. We need to find the present value (initial investment) required to reach the goal.

STEP 2

1. Understand the formula for compound interest.2. Identify the variables in the formula.3. Substitute the known values into the formula.4. Solve for the present value.5. Round the result to the nearest dollar.

STEP 3

STEP 4

Identify the variables in the formula.- A=59,000 A = 59,000 A=59,000 (the future value Jamal wants) - r=0.09 r = 0.09 r=0.09 (9% annual interest rate) - n=365 n = 365 n=365 (compounded daily) - t=7 t = 7 t=7 (years)

STEP 5

Substitute the known values into the formula:59,000=P(1+0.09365)365×7 59,000 = P \left(1 + \frac{0.09}{365}\right)^{365 \times 7} 59,000=P(1+3650.09​)365×7

STEP 6

STEP 7

Round the result to the nearest dollar.P≈31,313 P \approx 31,313 P≈31,313Jamal will need to invest \$31,313.

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

QuestionJamal wants to save $\$ 59,000$ for a down payment on a home. How much will he need to invest in an account with 9\% APR, compounding daily, in order to reach his goal in 7 years? Round to the nearest dollar.
He will need to invest \\square$
Question Help: Written Example

1. Jamal wants to save $59,000 for a down payment.
2. The account has an annual percentage rate (APR) of 9%.
3. The interest is compounded daily.
4. The investment period is 7 years.
5. We need to find the present value (initial investment) required to reach the goal.

1. Understand the formula for compound interest.
2. Identify the variables in the formula.
3. Substitute the known values into the formula.
4. Solve for the present value.
5. Round the result to the nearest dollar.

Identify the variables in the formula.
- $A = 59,000$ (the future value Jamal wants) - $r = 0.09$ (9% annual interest rate) - $n = 365$ (compounded daily) - $t = 7$ (years)

Substitute the known values into the formula:
$59,000 = P \left(1 + \frac{0.09}{365}\right)^{365 \times 7}$

Round the result to the nearest dollar.
$P \approx 31,313$
Jamal will need to invest \$31,313.