Arlen buys a home for $328,000 and makes a down payment of $33,000. The balance

Question

Arlen buys a home for $328,000 and makes a down payment of $33,000. The balance he finances with a 15 year mortgage with monthly payments and annual effective interest rate of 5.8%. There will be level payments followed by a final slightly reduced payment. Calculate the amount of interest that Arlen pays in the first 5 years of the loan. The answer is $73,797.79, please show clear steps. Please note- I noticed that this question was asked in the past before, and there is a seemingly through solution to the problem: http://www.chegg.com/homework-help/questions-and-answers/arlen-buys-home-328-000-makes-payment-33-000-balance-finances-15-year-mortgage-monthly-pay-q1636467 However, the principal payment is incorrect, because it should be $328,000 - $33,000

Explanation / Answer

Loan amt = Home cost - Down Payment = 328000-33000 = 295,000 Rate = 5.8%/12 nper = 15*12 = 180 periods 5 yr = 5*12 = 60 periods EAR =5.8%= (1+i/12)^(12) -1 So (1+i/12)^(12) = 1.058 ie 12 Log(1+i/12) = Log 1.058 ie Log (1+i/12) = 0.002040472 So 1+i/12 = ANtilog(0.002040472) = 1.0047 ie i = 12*0.0047 = 5.6513% CUMIPMT excel function Returns the cumulative interest paid on a loan between start_period and end_period. (Analysis ToolPak) It is CUMIPMT(Rate,nper,PV,start_period,end_period,type) So for 5 Yr Interest , Int is CUMIPMT(5.6513%/12,180,295000,1,60,0) = $73,797.83 Small diff in my answer is due to rounding off in excel..

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