Out of the following two plans, which one would be cheaper for the Mendozas:
The Mendozas wish to borrow $300,000 from a bank to help finance the purhcase of a house. Their banker has offered the following plans for their consideration:
(plan I) repay the loan in monthly installments over 30 years with
interest on the unpaid balance charged at 6.09%/year compounded monthly
(plan II) repay the loan in monthly installments over 15 years with interest on the unpaid balance charged at 5.76%/year compounded monthly.
Looking at the options it is easy to estimate which of them would be cheaper. The first plan requires payments over a longer duration of time and the interest rate is also higher. There is no doubt here that the second plan will be cheaper for the Mendozas.
As the question does not ask for a calculation of the exact difference in the two payments, there is no point in doing that. Just keep in mind that if the interest rate is higher for the same duration of time, the interest payment is higher. And for the same interest rate if the duration of payment is higher the interest paid is also higher.
The least interest is paid in the case where the interest payment is the least and payments also have to be made over the least duration of time.