Question

if a three - year car loan has the same interest rate as a six - year car loan, how do the monthly payments and the total prices compare for the two loans? the monthly payments for the three - year car loan will be

the monthly payments for the six - year car loan. the total amount for the three - year car loan will be

the total amount for the six - year car loan. (options for the first blank: greater than, less than, the same as; options for the second blank: greater than, less than, the same as)

Explanation:

Step1: Analyze Loan Payment Logic

For a car loan, the total amount (principal + interest) is repaid over the loan term. With the same interest rate and principal, a shorter loan term (3 years) means the total amount is spread over fewer months (36 months) compared to a longer term (6 years = 72 months).

Step2: Compare Monthly Payments

Since the total to repay (principal + interest) is similar (same rate, same principal), dividing by fewer months (36 vs. 72) results in a larger monthly payment for the 3 - year loan. So the monthly payments for the three - year car loan will be greater than the monthly payments for the six - year car loan.

Step3: Compare Total Payments

The total payment is the sum of all monthly payments. For the 3 - year loan, monthly payment ($M_3$) is higher, but number of months ($n_3 = 36$) is less. For the 6 - year loan, monthly payment ($M_6$) is lower, number of months ($n_6=72$) is more. But with the same interest rate, the total interest paid over 6 years will be more than over 3 years (because interest is charged over a longer time). However, for the monthly payment comparison part, as we saw, 3 - year monthly payments are greater.

Answer:

greater than