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As the compounding rate becomes lower and lower the future value of inflows approaches?
As the compounding rate decreases, the future value of inflows approaches the present value of those inflows. This occurs because lower compounding rates result in less growth over time, diminishing the effect of interest accumulation. Ultimately, if the compounding rate were to approach zero, the future value would converge to the total sum of the initial inflows without any interest or growth.
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If the compounding rate becomes lower and lower the future value of inflows approaches .?
the present value of the inflows
As the discount rate becomes higher the present value of inflows approaches?
As the discount rate increases, the present value of future cash inflows decreases. This is because higher discount rates reduce the value of future cash flows, reflecting the opportunity cost of capital and the time value of money. Ultimately, with a sufficiently high discount rate, the present value of future inflows can approach zero, indicating that those future cash inflows are less valuable in today's terms.
Why there is a limiting value in continuous compounding?
In continuous compounding, the limiting value arises from the mathematical property of exponential functions, where the process of compounding occurs infinitely over a time period. As the number of compounding intervals increases without bound, the future value of an investment approaches a limit defined by the exponential function ( e^{rt} ), where ( r ) is the interest rate and ( t ) is time. This limit reflects the maximum growth achievable under continuous compounding, illustrating that as compounding becomes more frequent, the value converges to a specific growth trajectory determined by the rate of interest. Thus, the limiting value represents the ultimate potential of an investment when compounded continuously.
Does the future value of an investment increases as the number of years of compounding at a positive rate of interest declines?
No, the future value of an investment does not increase as the number of years of compounding at a positive rate of interest declines. The future value is directly proportional to the number of compounding periods, so as the number of years of compounding decreases, the future value of the investment will also decrease.
What is the effect of changing the compounding period on the future value?
Changing the compounding period affects the future value of an investment by influencing how often interest is calculated and added to the principal. More frequent compounding periods, such as monthly instead of annually, generally result in a higher future value because interest is calculated more often, leading to interest on interest more frequently. Conversely, fewer compounding periods result in lower future values, as interest accumulates less frequently. Therefore, shorter compounding intervals typically enhance the growth of an investment over time.
How does the future value of a deposit subject to continuous compounding compare to the value obtained by annual compounding?
The future value of a deposit with continuous compounding is generally higher than that obtained through annual compounding, given the same interest rate and time frame. This is because continuous compounding calculates interest at every possible moment, effectively maximizing the amount of interest accrued over time. The formula for continuous compounding, ( FV = Pe^{rt} ), allows for exponential growth, while annual compounding relies on discrete intervals, resulting in less frequent interest calculations. Thus, for the same principal, interest rate, and duration, continuous compounding yields a greater future value.
If an investor had to choose between daily monthly or quarterly compounding which would you choose?
The greater the number of compounding periods, the larger the future value. The investor should choose daily compounding over monthly or quarterly.
More frequent compounding results in higher future values and lower present values than less frequent compounding at the same interest rate?
Yes
How does the frequency of interest compounding regardless of the rate of interest or period of accumulation affect the future value of any given amount?
The frequency of interest compounding significantly impacts the future value of an investment, as more frequent compounding results in interest being calculated and added to the principal more often. This leads to interest being earned on previously accrued interest, accelerating the growth of the investment. For example, compounding annually will yield a lower future value than compounding monthly or daily, even with the same interest rate and time period. Hence, increasing the compounding frequency enhances the overall returns on an investment.
Why the proses of discounting and compounding are related?
Discounting and compounding are related because both processes involve the time value of money, reflecting how the value of money changes over time. Compounding calculates the future value of an investment by applying interest over time, while discounting determines the present value of future cash flows by removing the effects of interest. Essentially, discounting is the reverse of compounding; where compounding grows an amount, discounting reduces it to its present value, both using the same interest rate concept. Together, they provide a comprehensive understanding of how money behaves over time in financial contexts.
When there is only one compounding period in a ordinary annuity the table factor for future value is always 1?
True
What is the difference between compounding and discounting?
Compounding finds the future value of a present value using a compound interest rate. Discounting finds the present value of some future value, using a discount rate. They are inverse relationships. This is perhaps best illustrated by demonstrating that a present value of some future sum is the amount which, if compounded using the same interest rate and time period, results in a future value of the very same amount.
