We receive a mortgage loan of $600,000 for 25 years.. The mortgage rate is 12% p

Question

We receive a mortgage loan of $600,000 for 25 years.. The mortgage rate is 12% per annum. First, derive the monthly payment you ought to make to the bank to amortize the loan. Secondly, compute the remaining amount you still owe the bank if you pay an additional single sum of $200,000 after 10 years. Thirdly, as part of this computation find how many more months you will pay the bank to induce the loan expire. Fourthly, if you accumulate a lot by year 15(end of the year) how much would you give additionally to the lender to eliminate the loan?

Explanation / Answer

First, derive the monthly payment you ought to make to the bank to amortize the loan. We have Loan amt = PV = 600,000, Loan tenure = nper = 25 yrs=25*12=300 months, Rate=12% pa = 12%/12 = 1% pm, ENd value of Loan = FV=0 SO Monthly Payment = PMT(Rate,nper,PV,FV) = PMT(1%,300,600000,0) = $(6,319) Negative sign means it is a Cash outflow. Secondly, compute the remaining amount you still owe the bank if you pay an additional single sum of $200,000 after 10 years. Here we need Future value at Y10 when PMT= $6,319, PV=600,000, nper =10Yr=10*12 =120 month, Rate = 1% pm SO Loan amt ay Y10 = FV(Rate,nper,PMT,PV) = FV(1%,120,-6319,600000) = $526,618 So Amt STill owed to Bank = $526,618 -$200,000 = $326,618 Thirdly, as part of this computation find how many more months you will pay the bank to induce the loan expire. So we have PV=326,618, PMT=6319,Rate=1%, FV=0 So No of months = nper(Rate,PMT,PV,FV) = nper(1%,-6319,326618,0) = 73.11 months Fourthly, if you accumulate a lot by year 15(end of the year) how much would you give additionally to the lender to eliminate the loan? Here we need Future value at Y15 when PMT= $6,319, PV=600,000, nper =15Yr=15*12 =180 month, Rate = 1% pm SO Loan amt ay Y15 = FV(Rate,nper,PMT,PV) = FV(1%,180,-6319,600000) = 440,634 So you will pay Lender 440,634 to eliminate the Loan at Y15

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