Math / Numbers & Operations

QuestionIf you borrow $\$ 300$ for 14 years at an annual interest rate of $4 \%$ , how much will you pay altogether?

Studdy Solution

STEP 1

1. The loan is compounded annually.
2. The interest rate is fixed at $4\%$ per annum.
3. The principal amount borrowed is $\$300$ .
4. The duration of the loan is 14 years.
5. The formula for compound interest is used to calculate the total amount paid.

STEP 2

1. Identify and define the variables for the compound interest formula.
2. Apply the compound interest formula to find the total amount owed after 14 years.
3. Calculate the total amount paid, including both principal and interest.

STEP 3

Identify and define the variables for the compound interest formula.
Let: - $P$ be the principal amount borrowed, which is \$300. - $ r $ be the annual interest rate, which is $4\%$ or $0.04$. - $ n $ be the number of times the interest is compounded per year, which is 1 (since it's compounded annually). - $ t $ be the number of years, which is 14.

STEP 4

Apply the compound interest formula to find the total amount owed after 14 years.
The compound interest formula is: $A = P \left(1 + \frac{r}{n}\right)^{nt}$
Since $n = 1$ , the formula simplifies to: $A = P (1 + r)^{t}$
Substitute the known values: $A = 300 \left(1 + 0.04\right)^{14}$

STEP 5

Calculate the expression inside the parentheses first: $1 + 0.04 = 1.04$
Then raise it to the power of 14: $1.04^{14}$

STEP 6

Use a calculator to compute $1.04^{14}$ : $1.04^{14} \approx 1.747422051$

STEP 7

Multiply this result by the principal amount to find the total amount owed: $A = 300 \times 1.747422051 \approx 524.23$
Thus, the total amount paid after 14 years will be approximately \$524.23.

STEP 8

Summarize the final result: The total amount paid after borrowing \$300 for 14 years at an annual interest rate of 4% is approximately \$524.23.

Was this helpful?

QuestionIf you borrow $\$ 300$ for 14 years at an annual interest rate of $4 \%$ , how much will you pay altogether?

Studdy Solution

STEP 1

1. The loan is compounded annually.
2. The interest rate is fixed at $4\%$ per annum.
3. The principal amount borrowed is $\$300$ .
4. The duration of the loan is 14 years.
5. The formula for compound interest is used to calculate the total amount paid.

STEP 2

1. Identify and define the variables for the compound interest formula.
2. Apply the compound interest formula to find the total amount owed after 14 years.
3. Calculate the total amount paid, including both principal and interest.

STEP 3

STEP 4

Apply the compound interest formula to find the total amount owed after 14 years.
The compound interest formula is: $A = P \left(1 + \frac{r}{n}\right)^{nt}$
Since $n = 1$ , the formula simplifies to: $A = P (1 + r)^{t}$
Substitute the known values: $A = 300 \left(1 + 0.04\right)^{14}$

STEP 5

Calculate the expression inside the parentheses first: $1 + 0.04 = 1.04$
Then raise it to the power of 14: $1.04^{14}$

STEP 6

Use a calculator to compute $1.04^{14}$ : $1.04^{14} \approx 1.747422051$

STEP 7

Multiply this result by the principal amount to find the total amount owed: $A = 300 \times 1.747422051 \approx 524.23$
Thus, the total amount paid after 14 years will be approximately \$524.23.

STEP 8

Summarize the final result: The total amount paid after borrowing \$300 for 14 years at an annual interest rate of 4% is approximately \$524.23.

Get Studdy

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.

QuestionIf you borrow $300\$ 300$300 for 14 years at an annual interest rate of 4%4 \%4%, how much will you pay altogether?

Studdy Solution

STEP 1

1. The loan is compounded annually.2. The interest rate is fixed at 4%4\%4% per annum.3. The principal amount borrowed is $300\$300$300.4. The duration of the loan is 14 years.5. The formula for compound interest is used to calculate the total amount paid.

STEP 2

1. Identify and define the variables for the compound interest formula.2. Apply the compound interest formula to find the total amount owed after 14 years.3. Calculate the total amount paid, including both principal and interest.

STEP 3

STEP 4

STEP 5

Calculate the expression inside the parentheses first: 1+0.04=1.04 1 + 0.04 = 1.04 1+0.04=1.04Then raise it to the power of 14: 1.0414 1.04^{14} 1.0414

STEP 6

Use a calculator to compute 1.0414 1.04^{14} 1.0414: 1.0414≈1.747422051 1.04^{14} \approx 1.747422051 1.0414≈1.747422051

STEP 7

Multiply this result by the principal amount to find the total amount owed: A=300×1.747422051≈524.23 A = 300 \times 1.747422051 \approx 524.23 A=300×1.747422051≈524.23Thus, the total amount paid after 14 years will be approximately \$524.23.

STEP 8

Summarize the final result: The total amount paid after borrowing \$300 for 14 years at an annual interest rate of 4% is approximately \$524.23.

Get Studdy

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.

QuestionIf you borrow $\$ 300$ for 14 years at an annual interest rate of $4 \%$ , how much will you pay altogether?

1. The loan is compounded annually.
2. The interest rate is fixed at $4\%$ per annum.
3. The principal amount borrowed is $\$300$ .
4. The duration of the loan is 14 years.
5. The formula for compound interest is used to calculate the total amount paid.

1. Identify and define the variables for the compound interest formula.
2. Apply the compound interest formula to find the total amount owed after 14 years.
3. Calculate the total amount paid, including both principal and interest.

Calculate the expression inside the parentheses first: $1 + 0.04 = 1.04$
Then raise it to the power of 14: $1.04^{14}$

Use a calculator to compute $1.04^{14}$ : $1.04^{14} \approx 1.747422051$

Multiply this result by the principal amount to find the total amount owed: $A = 300 \times 1.747422051 \approx 524.23$
Thus, the total amount paid after 14 years will be approximately \$524.23.