Question

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.

Answer 1

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.