You have taken out a standard 30-year mortgage (with monthly payments) for $374,

Question

You have taken out a standard 30-year mortgage (with monthly payments) for $374,000. The mortgage has a nominal annual interest rate of 4.68 percent (monthly compounding). For the first three months, you send your lender the required monthly payment plus an additional $500, $525, and $534, for months 1, 2, and 3, respectively. The additional amount directly reduces the amount outstanding on the mortgage at the end of each month. Determine the outstanding balance on the mortgage at the end of the third month. $371,00o O $371,500 $372,000 $372,500 $373,000

Explanation / Answer

HI in this question at first we will find out the monthly payment amout needs to be paid for this loan using excel

here Present value PV = -374,000 (since payment need to be made)

since payment is monthly hence total payments nper = 30*12 = 360

rate = 4.68% = 4.68/12 =0.39% monthly

so monthly payments = PMT(rate,nper,pv) = PMT(0.39%,360,-374000) =$1,935.21

now this monthly payment will contain both interest and principle so we will calculate that

interest after first month = 374000*0.39% = $1458.6

so principal payment = 1935.21- 1458.6= $476.61

so after one month outstanding amount = 374000-476.61 = 373,523.39

since additional $500 also deposited after one month hence net outstanding after 1 month = 373,523.39-500 = 373,023.39

Same way after second month outstanding amount = $372,017.97

and after third month outstanding amonut = 372017.97 - 1935.21 - 372017.97*0.39%-534 = $371,000

Hence option A is correct here

Thanks

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