Math / Algebra

QuestionFind the principal $P$ that will generate the given future value $A$ , where $A=\$ 14,000$ at $7 \%$ compounded daily for 9 years.
The principal P will be approximately $\$$ $\square$ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

1. We are using the compound interest formula.
2. The future value (A) is $14,000.
3. The interest rate (r) is 7% or 0.07.
4. Interest is compounded daily, so n = 365.
5. The time period (t) is 9 years.
6. We need to solve for the principal (P).
7. The answer should be rounded to two decimal places if necessary.

STEP 2

1. Recall the compound interest formula.
2. Substitute known values into the formula.
3. Algebraically isolate P.
4. Calculate the value of P.
5. Round the result to two decimal places if needed.

STEP 3

Recall the compound interest formula:
A = P(1 + r/n)^(nt)
Where: A = Future value P = Principal (initial investment) r = Annual interest rate (as a decimal) n = Number of times interest is compounded per year t = Number of years

STEP 4

Substitute the known values into the formula:
$14,000 = P(1 + 0.07/365)^(365*9)

STEP 5

To isolate P, we need to divide both sides by (1 + 0.07/365)^(3659):
P = $14,000 / (1 + 0.07/365)^(3659)

STEP 6

Now we can calculate the value of P:
P = $14,000 / (1 + 0.07/365)^(365*9) P =$ 14,000 / 1.8771147... P = $7,458.21...

STEP 7

Round the result to two decimal places:
P ≈ $7,458.21
The principal P that will generate a future value of $14,000 at 7% compounded daily for 9 years is approximately$ 7,458.21.

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QuestionFind the principal $P$ that will generate the given future value $A$ , where $A=\$ 14,000$ at $7 \%$ compounded daily for 9 years.
The principal P will be approximately $\$$ $\square$ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

STEP 2

1. Recall the compound interest formula.
2. Substitute known values into the formula.
3. Algebraically isolate P.
4. Calculate the value of P.
5. Round the result to two decimal places if needed.

STEP 3

Recall the compound interest formula:
A = P(1 + r/n)^(nt)
Where: A = Future value P = Principal (initial investment) r = Annual interest rate (as a decimal) n = Number of times interest is compounded per year t = Number of years

STEP 4

Substitute the known values into the formula:
$14,000 = P(1 + 0.07/365)^(365*9)

STEP 5

To isolate P, we need to divide both sides by (1 + 0.07/365)^(3659):
P = $14,000 / (1 + 0.07/365)^(3659)

STEP 6

Now we can calculate the value of P:
P = $14,000 / (1 + 0.07/365)^(365*9) P =$ 14,000 / 1.8771147... P = $7,458.21...

STEP 7

Round the result to two decimal places:
P ≈ $7,458.21
The principal P that will generate a future value of $14,000 at 7% compounded daily for 9 years is approximately$ 7,458.21.

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QuestionFind the principal PPP that will generate the given future value AAA, where A=$14,000A=\$ 14,000A=$14,000 at 7%7 \%7% compounded daily for 9 years.The principal P will be approximately $\$$ □\square□ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

STEP 2

1. Recall the compound interest formula.2. Substitute known values into the formula.3. Algebraically isolate P.4. Calculate the value of P.5. Round the result to two decimal places if needed.

STEP 3

Recall the compound interest formula:A = P(1 + r/n)^(nt)Where: A = Future value P = Principal (initial investment) r = Annual interest rate (as a decimal) n = Number of times interest is compounded per year t = Number of years

STEP 4

Substitute the known values into the formula:$14,000 = P(1 + 0.07/365)^(365*9)

STEP 5

To isolate P, we need to divide both sides by (1 + 0.07/365)^(365*9):P = $14,000 / (1 + 0.07/365)^(365*9)

STEP 6

Now we can calculate the value of P:P = 14,000/(1+0.07/365)(365∗9)P=14,000 / (1 + 0.07/365)^(365*9) P = 14,000/(1+0.07/365)(365∗9)P=14,000 / 1.8771147... P = $7,458.21...

STEP 7

Round the result to two decimal places:P ≈ $7,458.21 The principal P that will generate a future value of 14,000at714,000 at 7% compounded daily for 9 years is approximately 14,000at77,458.21.

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Start learning now

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

QuestionFind the principal $P$ that will generate the given future value $A$ , where $A=\$ 14,000$ at $7 \%$ compounded daily for 9 years.
The principal P will be approximately $\$$ $\square$ (Round to two decimal places as needed.)

1. Recall the compound interest formula.
2. Substitute known values into the formula.
3. Algebraically isolate P.
4. Calculate the value of P.
5. Round the result to two decimal places if needed.

Recall the compound interest formula:
A = P(1 + r/n)^(nt)
Where: A = Future value P = Principal (initial investment) r = Annual interest rate (as a decimal) n = Number of times interest is compounded per year t = Number of years

Substitute the known values into the formula:
$14,000 = P(1 + 0.07/365)^(365*9)

To isolate P, we need to divide both sides by (1 + 0.07/365)^(3659):
P = $14,000 / (1 + 0.07/365)^(3659)

Now we can calculate the value of P:
P = $14,000 / (1 + 0.07/365)^(365*9) P =$ 14,000 / 1.8771147... P = $7,458.21...

Round the result to two decimal places:
P ≈ $7,458.21
The principal P that will generate a future value of $14,000 at 7% compounded daily for 9 years is approximately$ 7,458.21.