Question

khadafi is borrowing $5,000 at an annual rate of 7% for a term of 4 years (48 months). what is the amount he will pay at the end of 4 years?
match the terms to the correct components.
principal a. $5,000
total interest to be paid b. $133.33
monthly payment c. $1,400
total amount repaid d. $6,400

Explanation:

Part 1: Matching Terms to Components

Principal

The principal is the initial amount borrowed. Here, Khadafi is borrowing $5,000, so principal matches with a. $5,000.

Total Interest to be Paid

To find total interest, we use the simple interest formula \( I = P \times r \times t \), where \( P = 5000 \), \( r = 0.07 \) (7% annual rate), and \( t = 4 \) years.

$$ I = 5000 \times 0.07 \times 4 = 1400 $$

So total interest to be paid matches with c. $1,400.

Monthly Payment

First, find the total amount to be repaid: \( A = P + I = 5000 + 1400 = 6400 \). Then, divide by the number of months (48) to get the monthly payment:

$$ \text{Monthly Payment} = \frac{6400}{48} \approx 133.33 $$

So monthly payment matches with b. $133.33.

Total Amount Repaid

Total amount repaid is principal plus total interest: \( 5000 + 1400 = 6400 \), so it matches with d. $6,400.

Part 2: Amount to Pay at the End of 4 Years

Using simple interest, the total amount \( A \) is given by \( A = P(1 + rt) \), where \( P = 5000 \), \( r = 0.07 \), \( t = 4 \).

$$ A = 5000(1 + 0.07 \times 4) = 5000(1 + 0.28) = 5000 \times 1.28 = 6400 $$

Final Matches and Answer

• Principal: a. $5,000
• Total Interest to be Paid: c. $1,400
• Monthly Payment: b. $133.33
• Total Amount Repaid: d. $6,400

The amount Khadafi will pay at the end of 4 years is $6,400.

Answer:

Part 1: Matching Terms to Components

Principal

The principal is the initial amount borrowed. Here, Khadafi is borrowing $5,000, so principal matches with a. $5,000.

Total Interest to be Paid

To find total interest, we use the simple interest formula \( I = P \times r \times t \), where \( P = 5000 \), \( r = 0.07 \) (7% annual rate), and \( t = 4 \) years.

$$ I = 5000 \times 0.07 \times 4 = 1400 $$

So total interest to be paid matches with c. $1,400.

Monthly Payment

First, find the total amount to be repaid: \( A = P + I = 5000 + 1400 = 6400 \). Then, divide by the number of months (48) to get the monthly payment:

$$ \text{Monthly Payment} = \frac{6400}{48} \approx 133.33 $$

So monthly payment matches with b. $133.33.

Total Amount Repaid

Total amount repaid is principal plus total interest: \( 5000 + 1400 = 6400 \), so it matches with d. $6,400.

Part 2: Amount to Pay at the End of 4 Years

Using simple interest, the total amount \( A \) is given by \( A = P(1 + rt) \), where \( P = 5000 \), \( r = 0.07 \), \( t = 4 \).

$$ A = 5000(1 + 0.07 \times 4) = 5000(1 + 0.28) = 5000 \times 1.28 = 6400 $$

Final Matches and Answer

• Principal: a. $5,000
• Total Interest to be Paid: c. $1,400
• Monthly Payment: b. $133.33
• Total Amount Repaid: d. $6,400

The amount Khadafi will pay at the end of 4 years is $6,400.