Charles needs a $10,000 loan in order to buy a car. Which loan option would allow him to pay the LEAST in interest?
Responses
A A 2-year loan with a 4.75% interest rate compounded annually.A 2-year loan with a 4.75% interest rate compounded annually.
B A 3-year loan with a 4.00% interest rate compounded annually.A 3-year loan with a 4.00% interest rate compounded annually.
C A 4-year loan with a 3.75% interest rate compounded annually.A 4-year loan with a 3.75% interest rate compounded annually.
D A 5-year loan with a 3.00% interest rate compounded annually.
To determine which loan option would allow Charles to pay the least in interest, we need to calculate the total amount of interest he would pay for each loan option.
For option A, the 2-year loan with a 4.75% interest rate compounded annually, the formula to calculate the total amount of interest paid is:
Total Interest = Principal * [(1 + Rate)^Time - 1]
Plugging in the values, we get:
Total Interest = $10,000 * [(1 + 0.0475)^2 - 1] = $954.38
For option B, the 3-year loan with a 4.00% interest rate compounded annually, we calculate:
Total Interest = $10,000 * [(1 + 0.04)^3 - 1] = $1,216.00
For option C, the 4-year loan with a 3.75% interest rate compounded annually:
Total Interest = $10,000 * [(1 + 0.0375)^4 - 1] = $1,413.84
For option D, the 5-year loan with a 3.00% interest rate compounded annually:
Total Interest = $10,000 * [(1 + 0.03)^5 - 1] = $1,537.04
Comparing the total interest paid for each option, it can be seen that option A has the lowest amount of interest, with $954.38. Hence, option A, the 2-year loan with a 4.75% interest rate compounded annually, would allow Charles to pay the least in interest. Answer: A.
In order to determine which loan option would allow Charles to pay the least in interest, we need to calculate the amount of interest for each option.
Option A:
Principal: $10,000
Interest rate: 4.75%
Time: 2 years
Compound interest: annually
Interest = Principal * (1 + (Interest Rate / 100))^Time - Principal
Interest A = $10,000 * (1 + (4.75 / 100))^2 - $10,000
Option B:
Principal: $10,000
Interest rate: 4.00%
Time: 3 years
Compound interest: annually
Interest B = $10,000 * (1 + (4.00 / 100))^3 - $10,000
Option C:
Principal: $10,000
Interest rate: 3.75%
Time: 4 years
Compound interest: annually
Interest C = $10,000 * (1 + (3.75 / 100))^4 - $10,000
Option D:
Principal: $10,000
Interest rate: 3.00%
Time: 5 years
Compound interest: annually
Interest D = $10,000 * (1 + (3.00 / 100))^5 - $10,000
Now, calculate the interest for each option:
Interest A = $10,000 * (1 + (4.75 / 100))^2 - $10,000
Interest B = $10,000 * (1 + (4.00 / 100))^3 - $10,000
Interest C = $10,000 * (1 + (3.75 / 100))^4 - $10,000
Interest D = $10,000 * (1 + (3.00 / 100))^5 - $10,000
After calculating, we can compare the interest values for each option. The option with the lowest interest amount would allow Charles to pay the least in interest.
To determine which loan option would allow Charles to pay the least in interest, we need to calculate the total interest paid for each loan option.
To calculate the total interest paid, we can use the formula for compound interest:
Total Interest Paid = Principal * (1 + (interest rate / number of compounding periods))^(number of compounding periods * number of years) - Principal
Now, let's calculate the total interest paid for each loan option:
Option A:
Principal = $10,000
Interest rate = 4.75% = 0.0475
Number of compounding periods = 1 (compounded annually)
Number of years = 2
Total Interest Paid = $10,000 * (1 + (0.0475 / 1))^(1 * 2) - $10,000
Option B:
Principal = $10,000
Interest rate = 4.00% = 0.04
Number of compounding periods = 1 (compounded annually)
Number of years = 3
Total Interest Paid = $10,000 * (1 + (0.04 / 1))^(1 * 3) - $10,000
Option C:
Principal = $10,000
Interest rate = 3.75% = 0.0375
Number of compounding periods = 1 (compounded annually)
Number of years = 4
Total Interest Paid = $10,000 * (1 + (0.0375 / 1))^(1 * 4) - $10,000
Option D:
Principal = $10,000
Interest rate = 3.00% = 0.03
Number of compounding periods = 1 (compounded annually)
Number of years = 5
Total Interest Paid = $10,000 * (1 + (0.03 / 1))^(1 * 5) - $10,000
Now, we can calculate the total interest paid for each option:
Total Interest Paid for Option A = $10,000 * (1 + 0.0475)^(2) - $10,000
Total Interest Paid for Option B = $10,000 * (1 + 0.04)^(3) - $10,000
Total Interest Paid for Option C = $10,000 * (1 + 0.0375)^(4) - $10,000
Total Interest Paid for Option D = $10,000 * (1 + 0.03)^(5) - $10,000
By calculating the total interest paid for each option, you can compare the values to determine which loan option would allow Charles to pay the least in interest.