Solved on Mar 12, 2024

Find the value of $A$ using the given values: $P=150,000$ , $r=0.35$ , $n=4$ , and $Y=30$ . Round the result to the nearest whole number.

STEP 1

Assumptions
1. The principal amount $P$ is $150,000.<br />2. The annual interest rate$ r $is$ 0.35 $(or$ 35\% $).<br />3. The number of times the interest is compounded per year$ n $is$ 4 $.<br />4. The number of years$ Y $is$ 30$.
5. We need to substitute these values into the given compound interest formula and simplify.
6. The final answer should be rounded to the nearest whole number.

STEP 2

Substitute the given values into the compound interest formula.
$A = P\left(1+\frac{r}{n}\right)^{nY}$
$A = 150,000\left(1+\frac{0.35}{4}\right)^{4 \cdot 30}$

STEP 3

Calculate the fraction inside the parentheses.
$\frac{r}{n} = \frac{0.35}{4}$

STEP 4

Simplify the fraction.
$\frac{0.35}{4} = 0.0875$

STEP 5

Substitute the simplified fraction back into the formula.
$A = 150,000\left(1+0.0875\right)^{4 \cdot 30}$

STEP 6

Add $1$ to the decimal.
$1 + 0.0875 = 1.0875$

STEP 7

Substitute the sum back into the formula.
$A = 150,000 \cdot 1.0875^{4 \cdot 30}$

STEP 8

Calculate the exponent $4 \cdot 30$ .
$4 \cdot 30 = 120$

STEP 9

Substitute the exponent back into the formula.
$A = 150,000 \cdot 1.0875^{120}$

STEP 10

Calculate the value of $1.0875^{120}$ using a calculator.
$1.0875^{120} \approx 41.960274$

STEP 11

Substitute the calculated value back into the formula.
$A = 150,000 \cdot 41.960274$

STEP 12

Multiply $150,000$ by $41.960274$ to find the value of $A$ .
$A \approx 150,000 \cdot 41.960274$

STEP 13

Perform the multiplication to find the approximate value of $A$ .
$A \approx 6,294,041.1$

STEP 14

Round the result to the nearest whole number.
$A \approx 6,294,041$
The value of $A$ rounded to the nearest whole number is $6,294,041$ .
Therefore, the correct answer is (A) $6,294,041$ .

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Find the value of $A$ using the given values: $P=150,000$ , $r=0.35$ , $n=4$ , and $Y=30$ . Round the result to the nearest whole number.

STEP 1

STEP 2

Substitute the given values into the compound interest formula.
$A = P\left(1+\frac{r}{n}\right)^{nY}$
$A = 150,000\left(1+\frac{0.35}{4}\right)^{4 \cdot 30}$

STEP 3

Calculate the fraction inside the parentheses.
$\frac{r}{n} = \frac{0.35}{4}$

STEP 4

Simplify the fraction.
$\frac{0.35}{4} = 0.0875$

STEP 5

Substitute the simplified fraction back into the formula.
$A = 150,000\left(1+0.0875\right)^{4 \cdot 30}$

STEP 6

Add $1$ to the decimal.
$1 + 0.0875 = 1.0875$

STEP 7

Substitute the sum back into the formula.
$A = 150,000 \cdot 1.0875^{4 \cdot 30}$

STEP 8

Calculate the exponent $4 \cdot 30$ .
$4 \cdot 30 = 120$

STEP 9

Substitute the exponent back into the formula.
$A = 150,000 \cdot 1.0875^{120}$

STEP 10

Calculate the value of $1.0875^{120}$ using a calculator.
$1.0875^{120} \approx 41.960274$

STEP 11

Substitute the calculated value back into the formula.
$A = 150,000 \cdot 41.960274$

STEP 12

Multiply $150,000$ by $41.960274$ to find the value of $A$ .
$A \approx 150,000 \cdot 41.960274$

STEP 13

Perform the multiplication to find the approximate value of $A$ .
$A \approx 6,294,041.1$

STEP 14

Round the result to the nearest whole number.
$A \approx 6,294,041$
The value of $A$ rounded to the nearest whole number is $6,294,041$ .
Therefore, the correct answer is (A) $6,294,041$ .

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Find the value of AAA using the given values: P=150,000P=150,000P=150,000, r=0.35r=0.35r=0.35, n=4n=4n=4, and Y=30Y=30Y=30. Round the result to the nearest whole number.

STEP 1

STEP 2

Substitute the given values into the compound interest formula.A=P(1+rn)nYA = P\left(1+\frac{r}{n}\right)^{nY}A=P(1+nr​)nYA=150,000(1+0.354)4⋅30A = 150,000\left(1+\frac{0.35}{4}\right)^{4 \cdot 30}A=150,000(1+40.35​)4⋅30

STEP 3

Calculate the fraction inside the parentheses.rn=0.354\frac{r}{n} = \frac{0.35}{4}nr​=40.35​

STEP 4

Simplify the fraction.0.354=0.0875\frac{0.35}{4} = 0.087540.35​=0.0875

STEP 5

Substitute the simplified fraction back into the formula.A=150,000(1+0.0875)4⋅30A = 150,000\left(1+0.0875\right)^{4 \cdot 30}A=150,000(1+0.0875)4⋅30

STEP 6

Add 111 to the decimal.1+0.0875=1.08751 + 0.0875 = 1.08751+0.0875=1.0875

STEP 7

Substitute the sum back into the formula.A=150,000⋅1.08754⋅30A = 150,000 \cdot 1.0875^{4 \cdot 30}A=150,000⋅1.08754⋅30

STEP 8

Calculate the exponent 4⋅304 \cdot 304⋅30.4⋅30=1204 \cdot 30 = 1204⋅30=120

STEP 9

Substitute the exponent back into the formula.A=150,000⋅1.0875120A = 150,000 \cdot 1.0875^{120}A=150,000⋅1.0875120

STEP 10

Calculate the value of 1.08751201.0875^{120}1.0875120 using a calculator.1.0875120≈41.9602741.0875^{120} \approx 41.9602741.0875120≈41.960274

STEP 11

Substitute the calculated value back into the formula.A=150,000⋅41.960274A = 150,000 \cdot 41.960274A=150,000⋅41.960274

STEP 12

Multiply 150,000150,000150,000 by 41.96027441.96027441.960274 to find the value of AAA.A≈150,000⋅41.960274A \approx 150,000 \cdot 41.960274A≈150,000⋅41.960274

STEP 13

Perform the multiplication to find the approximate value of AAA.A≈6,294,041.1A \approx 6,294,041.1A≈6,294,041.1

STEP 14

Round the result to the nearest whole number.A≈6,294,041A \approx 6,294,041A≈6,294,041The value of AAA rounded to the nearest whole number is 6,294,0416,294,0416,294,041.Therefore, the correct answer is (A) 6,294,0416,294,0416,294,041.

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Find the value of $A$ using the given values: $P=150,000$ , $r=0.35$ , $n=4$ , and $Y=30$ . Round the result to the nearest whole number.

Substitute the given values into the compound interest formula.
$A = P\left(1+\frac{r}{n}\right)^{nY}$
$A = 150,000\left(1+\frac{0.35}{4}\right)^{4 \cdot 30}$

Calculate the fraction inside the parentheses.
$\frac{r}{n} = \frac{0.35}{4}$

Simplify the fraction.
$\frac{0.35}{4} = 0.0875$

Substitute the simplified fraction back into the formula.
$A = 150,000\left(1+0.0875\right)^{4 \cdot 30}$

Add $1$ to the decimal.
$1 + 0.0875 = 1.0875$

Substitute the sum back into the formula.
$A = 150,000 \cdot 1.0875^{4 \cdot 30}$

Calculate the exponent $4 \cdot 30$ .
$4 \cdot 30 = 120$

Substitute the exponent back into the formula.
$A = 150,000 \cdot 1.0875^{120}$

Calculate the value of $1.0875^{120}$ using a calculator.
$1.0875^{120} \approx 41.960274$

Substitute the calculated value back into the formula.
$A = 150,000 \cdot 41.960274$

Multiply $150,000$ by $41.960274$ to find the value of $A$ .
$A \approx 150,000 \cdot 41.960274$

Perform the multiplication to find the approximate value of $A$ .
$A \approx 6,294,041.1$

Round the result to the nearest whole number.
$A \approx 6,294,041$
The value of $A$ rounded to the nearest whole number is $6,294,041$ .
Therefore, the correct answer is (A) $6,294,041$ .