Continuous compound interest with additional transactions

In summary, the accountants at HR office of the Sirius Cybernetics Corporation have determined that the company would need an additional $10 billion in its pension fund account by the end of year 2030. To achieve this, the company will make regular contributions in 20 equal yearly installments, assuming the fund's balance will grow continuously at a rate of 10% a year. This would result in a yearly contribution of $309.32 million. However, the CFO of the company decides to "manage" the pension accounting by assuming a more aggressive 12.5% projected yearly growth rate, resulting in a yearly contribution of $218.12 million.
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lionsgirl12
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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.

Homework Equations


The Attempt at a Solution

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

FAQ: Continuous compound interest with additional transactions

What is continuous compound interest?

Continuous compound interest is a method of calculating interest on a principal amount that is continuously compounded, meaning that interest is earned on the initial investment as well as any accumulated interest. This leads to faster growth of the investment compared to simple and compound interest methods.

What are additional transactions in continuous compound interest?

Additional transactions refer to any deposits or withdrawals made into or from the initial investment. These can affect the amount of interest earned on the investment, as the interest is continuously compounded on the new balance after each transaction.

How is continuous compound interest with additional transactions calculated?

The formula used for continuous compound interest with additional transactions is A = P*e^(rt), where A is the final amount, P is the principal amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time period in years. This formula takes into account any additional transactions made during the time period.

What is the benefit of using continuous compound interest with additional transactions?

The benefit of using continuous compound interest with additional transactions is that it leads to faster growth of the investment compared to other methods. This is because the interest is continuously compounded, allowing for more frequent and greater compounding of interest on the initial investment and any additional transactions. This can result in a significantly higher return on investment over time.

Are there any limitations to using continuous compound interest with additional transactions?

One limitation of using continuous compound interest with additional transactions is that it assumes a constant annual interest rate. In reality, interest rates can fluctuate, which can affect the accuracy of the calculations. Additionally, it may not be suitable for short-term investments as the impact of additional transactions may be minimal on the overall growth of the investment.

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