We receive a mortgage loan of $300,000 for 25 year.. If the monthly payment we o

Question

We receive a mortgage loan of $300,000 for 25 year.. If the monthly payment we ought to make to the bank to amortize the loan is 4,000, compute the annual yield.. Secondly, compute the remaining amount we still owe the bank, if we pay an additional single sum of $50,000 after 14years. Thirdly, as part of this computation, find how many more months, we will pay the bank to induce the loan to expire. Fourthly, if we accumulate a lot by year 8 (end of the year), how much would we give additionally to the lender to eliminate the loan?

Explanation / Answer

Ans;

We receive a mortgage loan of $300,000 for 30 years.. The mortgage rate is 12% per annum. First, derive the monthly payment we ought to make to the bank to amortize the loan. Secondly, compute the remaining amount we still owe the bank, if we pay an additional single sum of $40,000 after 7 years. Thirdly, as part of this computation find how many more months, we will pay the bank to induce the loan expire. Fourthly, if we accumulate a lot by year 12(end of the year)

We have Loan amt = PV = $300,000. Futire value FV of loan = 0
Rate = 12% pa = 12%/12 = 1% pm
Tenure = 30 Yrs. So nper = 30*12=360 months
(a) So Monthly Payment = PMT(Rate,nper,PV,FV)
= PMT(1%,360,-300000,0) = $3,086 pm ...............Ans (a)

(b) Princiapl at end of 7 yrs (12*7=84 periods) = FV(Rate,nper,PMT,PV)
= FV(1%,84,-3086,300000)
= $288,762
Addl $40,000 is paid here
So New priciapal is $288,762-40000 = $248,762 ...........Ans (b)

(c) Now Principal is $248,762. PMT is still 3086, So remaining tenure nper is
nper(rate,PMT,PV,FV) = nper(1%,-3086,248762,0) = 165 months .......Ans (c)

(d) At end of Y7, princiapl is $288,762.
AT start of Y8, Pricniapl is $248,762
SO From Start of Y8 to end of Y12, no of yrs = 5. ie 5*12 = 60 periods
Princiapl at end of 12 yrs (60 periods) = FV(Rate,nper,PMT,PV)
= FV(1%,60,-3086,248762) = $199,893
So AMt balance is 300,000- $199,893 = $100,107

So we have to give addlly $100,107 at end of Y12 to extinguih the loan

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