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Continuous compound interest with additional transactions

  1. Sep 8, 2010 #1
    1. The accountants at HR office of the Sirius Cybernetics Corporation have determined that the company would need additional $10 billion in its pension fund account over and above the current projected amount at the end of year 2030.

    (a) Assuming the fund's balance will be growing, compounds continuously, at a rate of 10% a year, and the company will make regular contribution in 20 equal yearly installments over the 20-year period. How much is the company's yearly contribution?

    (b) Not wanting to pony up the amount found in (a), the CFO of the company decides to "manage" (using a classic, but legal, way of gaming the accounting system in order to lower short-term expenses and, therefore, increase currently reported profit) the pension accounting by assuming a more aggressive 12.5% projected yearly growth rate, rather than 10%. How much is the company's would-be yearly outlay under the new growth assumption? Hint: In each case, solve the IVP with P(0) = $0; and then use P(20) = $10 billion to solve for the yearly contribution.

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 8, 2010 #2


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    Gold Member

    Where is your work and what formulas would you like to use?
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