# Continuous compound interest with additional transactions

1. Sep 8, 2010

### lionsgirl12

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. Sep 8, 2010

### cronxeh

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