Math / Algebra

QuestionSuppose that $\$ 14,000$ is deposited for seven years at $3 \%$ APR. Calculate the interest earned if interest is compounded monthly. Round your answer to the nearest cent. Formulas

Studdy Solution

STEP 1

1. The principal amount $P$ is \ $14,000.<br />2. The annual percentage rate (APR)$ r $is 3%, or 0.03 as a decimal.<br />3. The interest is compounded monthly, which means there are 12 compounding periods per year.<br />4. The total time$ t is 7 years.
5. The formula for compound interest is $ A = P \left(1 + \frac{r}{n}\right)^{nt} $, where A $is the amount of money accumulated after$ n $years, including interest.<br />6. The interest earned is the accumulated amount$ A $minus the principal$ P$.

STEP 2

1. Identify and substitute the given values into the compound interest formula.
2. Calculate the monthly interest rate.
3. Determine the total number of compounding periods.
4. Calculate the accumulated amount $A$ using the compound interest formula.
5. Subtract the principal $P$ from $A$ to find the interest earned.
6. Round the interest earned to the nearest cent.

STEP 3

Identify and substitute the given values into the compound interest formula:
$P = 14000, \quad r = 0.03, \quad n = 12, \quad t = 7$
The formula for compound interest is:
$A = P \left(1 + \frac{r}{n}\right)^{nt}$

STEP 4

Calculate the monthly interest rate.
$\frac{r}{n} = \frac{0.03}{12} = 0.0025$

STEP 5

Determine the total number of compounding periods.
$nt = 12 \times 7 = 84$

STEP 6

Calculate the accumulated amount $A$ using the compound interest formula.
$A = 14000 \left(1 + 0.0025\right)^{84}$

STEP 7

Evaluate the expression inside the parentheses and then raise it to the power of 84.
$1 + 0.0025 = 1.0025$
$1.0025^{84}$

STEP 8

Compute $1.0025^{84}$ .
Using a calculator:
$1.0025^{84} \approx 1.221386$

STEP 9

Finally, calculate the accumulated amount $A$ .
$A = 14000 \times 1.221386 \approx 17199.40$

STEP 10

Subtract the principal $P$ from $A$ to find the interest earned.
$\text{Interest Earned} = A - P = 17199.40 - 14000 = 3199.40$

STEP 11

Round the interest earned to the nearest cent.
The interest earned is approximately:
$\boxed{3199.40}$

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QuestionSuppose that $\$ 14,000$ is deposited for seven years at $3 \%$ APR. Calculate the interest earned if interest is compounded monthly. Round your answer to the nearest cent. Formulas

Studdy Solution

STEP 1

STEP 2

STEP 3

Identify and substitute the given values into the compound interest formula:
$P = 14000, \quad r = 0.03, \quad n = 12, \quad t = 7$
The formula for compound interest is:
$A = P \left(1 + \frac{r}{n}\right)^{nt}$

STEP 4

Calculate the monthly interest rate.
$\frac{r}{n} = \frac{0.03}{12} = 0.0025$

STEP 5

Determine the total number of compounding periods.
$nt = 12 \times 7 = 84$

STEP 6

Calculate the accumulated amount $A$ using the compound interest formula.
$A = 14000 \left(1 + 0.0025\right)^{84}$

STEP 7

Evaluate the expression inside the parentheses and then raise it to the power of 84.
$1 + 0.0025 = 1.0025$
$1.0025^{84}$

STEP 8

Compute $1.0025^{84}$ .
Using a calculator:
$1.0025^{84} \approx 1.221386$

STEP 9

Finally, calculate the accumulated amount $A$ .
$A = 14000 \times 1.221386 \approx 17199.40$

STEP 10

Subtract the principal $P$ from $A$ to find the interest earned.
$\text{Interest Earned} = A - P = 17199.40 - 14000 = 3199.40$

STEP 11

Round the interest earned to the nearest cent.
The interest earned is approximately:
$\boxed{3199.40}$

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QuestionSuppose that $14,000\$ 14,000$14,000 is deposited for seven years at 3%3 \%3% APR. Calculate the interest earned if interest is compounded monthly. Round your answer to the nearest cent. Formulas

Studdy Solution

STEP 1

STEP 2

STEP 3

Identify and substitute the given values into the compound interest formula:P=14000,r=0.03,n=12,t=7 P = 14000, \quad r = 0.03, \quad n = 12, \quad t = 7 P=14000,r=0.03,n=12,t=7The formula for compound interest is:A=P(1+rn)nt A = P \left(1 + \frac{r}{n}\right)^{nt} A=P(1+nr​)nt

STEP 4

Calculate the monthly interest rate.rn=0.0312=0.0025 \frac{r}{n} = \frac{0.03}{12} = 0.0025 nr​=120.03​=0.0025

STEP 5

Determine the total number of compounding periods.nt=12×7=84 nt = 12 \times 7 = 84 nt=12×7=84

STEP 6

Calculate the accumulated amount AAA using the compound interest formula.A=14000(1+0.0025)84 A = 14000 \left(1 + 0.0025\right)^{84} A=14000(1+0.0025)84

STEP 7

Evaluate the expression inside the parentheses and then raise it to the power of 84.1+0.0025=1.0025 1 + 0.0025 = 1.0025 1+0.0025=1.00251.002584 1.0025^{84} 1.002584

STEP 8

Compute 1.002584 1.0025^{84} 1.002584.Using a calculator:1.002584≈1.221386 1.0025^{84} \approx 1.221386 1.002584≈1.221386

STEP 9

Finally, calculate the accumulated amount AAA.A=14000×1.221386≈17199.40 A = 14000 \times 1.221386 \approx 17199.40 A=14000×1.221386≈17199.40

STEP 10

Subtract the principal PPP from AAA to find the interest earned.Interest Earned=A−P=17199.40−14000=3199.40 \text{Interest Earned} = A - P = 17199.40 - 14000 = 3199.40 Interest Earned=A−P=17199.40−14000=3199.40

STEP 11

Round the interest earned to the nearest cent.The interest earned is approximately:3199.40 \boxed{3199.40} 3199.40​

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QuestionSuppose that $\$ 14,000$ is deposited for seven years at $3 \%$ APR. Calculate the interest earned if interest is compounded monthly. Round your answer to the nearest cent. Formulas

Identify and substitute the given values into the compound interest formula:
$P = 14000, \quad r = 0.03, \quad n = 12, \quad t = 7$
The formula for compound interest is:
$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Calculate the monthly interest rate.
$\frac{r}{n} = \frac{0.03}{12} = 0.0025$

Determine the total number of compounding periods.
$nt = 12 \times 7 = 84$

Calculate the accumulated amount $A$ using the compound interest formula.
$A = 14000 \left(1 + 0.0025\right)^{84}$

Evaluate the expression inside the parentheses and then raise it to the power of 84.
$1 + 0.0025 = 1.0025$
$1.0025^{84}$

Compute $1.0025^{84}$ .
Using a calculator:
$1.0025^{84} \approx 1.221386$

Finally, calculate the accumulated amount $A$ .
$A = 14000 \times 1.221386 \approx 17199.40$

Subtract the principal $P$ from $A$ to find the interest earned.
$\text{Interest Earned} = A - P = 17199.40 - 14000 = 3199.40$

Round the interest earned to the nearest cent.
The interest earned is approximately:
$\boxed{3199.40}$