question archive A company has borrowed $A and has agreed to pay interest on the loan every 3-months at j4 = 8% and pay back the $A in one lump sum at the end of 11 years
A company has borrowed $A and has agreed to pay interest on the loan every 3-months at j4 = 8% and pay back the $A in one lump sum at the end of 11 years
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A company has borrowed $A and has agreed to pay interest on the loan every 3-months at j4 = 8% and pay back the $A in one lump sum at the end of 11 years. The company will make quarterly deposits in a sinking fund earning j4 = 4% to accumulate to $A by the end of 11 years. If the book value of the loan after 5 years is $81,485, what is the value of A? (Answer to the nearest $100)
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The answer is 249 200
Step-by-step explanation
As specifically stated in the Question that Interest payment is on quarterly rest.
Secondly Interest rate is always mentioned on per annum bais hence 8% interest is on per annumm basis.
Hence on Quarterly rest basis it will be 8% /4 Quarter = 2%
As PV of Loan as on End of the 5th Year is 81485 given
By Using NPV formulae NPV( 2%, 20 years) = 81485
Let the Interest payable per quarter is XNPV ( 2%, X, 20 Years ) = 81485
X = 4984
As the 4984 is the interest on Quarterly rest,i.e. interest payable
X*2% = 4984
Hence X( Loan Value in gross) = 249200
