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Sinking Fund Question from Kellison

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  • Sinking Fund Question from Kellison

    Hi 27 from Kellison 6.4, "A payment of $36,000 is made at the end of each year for 31 years to repay a loan of $400,000. If the borrower replaces the capital by means of a sinking fund earning 3% effective, find the effective rate paid to the lender on the loan." Ans: 7%
    For this problem I assumed that the value of the sinking fund will be the amount of the loan at the end of the 31 years (400,000), and I said that the sinking fund deposit is 36000- 36000i... this question did not work out for me, can someone help me? thanks.

  • #2
    First calculate the annual payments it would take to pay off the sinking fund. Then subtract that from the 36,000 to get the interest payments to the lender. Divide by the principal, and you get i=.07.

    (I was stumped too; I think the wording in the problem is a little vague)
    Last edited by Arnold Kim; October 26 2005, 09:31 PM. Reason: came up with a quicker and more efficient answer to the question

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    • #3
      Not exactly sure what you guys are doing.

      Your payment going into the sinking fund is 36000-400000i.
      This accumulated at 3% for 31 years is supposed to pay off the 400000.

      (36000 - 400000i)s(angle 31 at 3%) = 400000

      Solve for i.
      Whether you are the lion or the gazelle, when the sun comes up, you better be running.

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