You plan to purchase a $330,000 house using either a 30-year mortgage obtained from your local savings bank with a rate of 8.00 percent, or a 20-year mortgage with a rate of 7.00 percent. You will make a down payment of 20 percent of the purchase price. a. Calculate the amount of interest and, separately, principal paid on each mortgage. What is the difference in interest paid

30 year mortgage

down payment = $330,000 x 20% = $66,000

debt = $330,000 - $66,000  = $264,000

monthly payment = $264,000 / 136.2834 (PV annuity factor, 360 periods, 0.667%) = $1,937.14

total payments = $1,937.14 x 360 = $697,370.40

total interest paid = $697,370.40 - $264,000 = $433,370.40

20 year mortgage

down payment = $330,000 x 20% = $66,000

debt = $330,000 - $66,000  = $264,000

monthly payment = $264,000 / 128.9825 (PV annuity factor, 240 periods, 0.583%) = $2,046.79

total payments = $2,046.79 x 240 = $491,229.60

total interest paid = $491,229.60 - $264,000 = $227,229.60

the 20 year mortgage charges $433,370.40 - $227,229.60 = $206,140.80 less interest

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