# Which loan repayment plan should the Mendozas select? The Mendozas wish to borrow \$300,000 from a bank to help finance the purhcase of a house. Their bank has offered the following plans for their consideration: 1. Repay the loan in monthly installments over 30 years with interest on the unpaid balance charged at 6.09%/year compounded monthly 2. Repay the loan in monthly installments over 15 years with interest on the unpaid balance charged at 5.76%/year compounded monthly.What is the monthly repayment for each plan and the total amount to be repaid for each plan?

The Mendozas have two plans to select from for the \$300,000 they want to borrow.

The formula for calculating the monthly payment is: [(p*r)(1+r)^n]/[(1+r)^n - 1], where p = amount borrowed, r = rate of interest per month and n = number of months.

• In the first plan, the tenure is 30 years or 360 months at 6.09/12 = 0.5075% per month.

The monthly payment is: (300000*0.005075*(1.005075)^360/((1.005075)^360 - 1) = \$1816.04

The total payment would be: \$653,776.92

• In the second plan the tenure is 15 years or 180 months at 5.76/12 = 0.48%

The monthly payment is (300000*0.0048*(1.0048)^180/((1.0048)^180 - 1) = \$2492.83

The total payment would be : \$448,710.65

Therefore the Mendozas should choose plan 2 as it saves \$205,006 over the course of their repayment, though the monthly payment is slightly higher.

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