compounding period

(noun)

The length of time between the points at which interest is paid.

Related Terms

Examples of compounding period in the following topics:

  • Calculating Values for Different Durations of Compounding Periods

    • For example, the interest rate could be 12% compounded monthly, but one period is one year.
    • This atom will discuss how to handle different compounding periods.
    • Luckily, it's possible to incorporate compounding periods into the standard time-value of money formula.
    • The equation follows the same logic as the standard formula. r/n is simply the nominal interest per compounding period, and nt represents the total number of compounding periods.
    • Calculate the present and future value of something that has different compounding periods

  • Calculating Values for Fractional Time Periods

    • Up to this point, we have implicitly assumed that the number of periods in question matches to a multiple of the compounding period.
    • Compounding periods can be any length of time, and the length of the period affects the rate at which interest accrues.
    • Suppose the compounding period is one year, starting January1, 2012.
    • In this case, you need to find the amount of money that is actually in the account, so you round the number of periods down to the nearest whole number (assuming one period is the same as a compounding period; if not, round down to the nearest compounding period).
    • Even if interest compounds every period, and you are asked to find the balance at the 6.9999th period, you need to round down to 6.

  • Modular 12 Arithmetic

    • The compound period (also called the 16-bar period because its typical form is 16 bars long), is made of two themes instead of two phrases.
    • The first type of compound period is comprised of two sentences: the first ends with an HC or (less frequently) an IAC, and the second ends with a PAC.
    • A prototypical example of a compound period composed of two sentences is Mozart's Piano Sonata in F major, K. 332, II., mm. 1–8.
    • Similarly, a compound period can be comprised of two Hybrid 1 themes (antecedent–continuation)
    • At other times, a compound theme is set to such a slow tempo that it takes only 8 bars (like the compound period in Mozart's K. 332, above).

  • Interest Compounded Continuously

    • The amount of interest earned increases with each compounding period.
    • The more frequent the compounding periods the more interest is accrued.
    • In this situation the amount of money in the account will be given by $(1+\frac{1}{n})^n$ where $n$ is the number of compounding periods and $\frac{1}{n}$ is the rate per compounding period.
    • The formula for compound interest with the number of compounding periods going to infinity yields the formula for compounding continuously.
    • Graph of interest accrued under differing number of compounding periods per year

  • Multi-Period Investment

    • Multi-period investments require an understanding of compound interest, incorporating the time value of money over time.
    • The future value is simply the present value applied to the interest rate compounded one time.
    • With multi-periods in mind, interest begins to compound.
    • Compound interest simple means that the interest from the first period is added to the future present value, and the interest rate the next time around is now being applied to a larger amount.
    • Normalizing expected returns in present value terms (or projecting future returns over multiple time periods of compounding interest) paints a clearer and more accurate picture of the actual worth of a given investment opportunity.

  • Number of Periods

    • In , nrepresents the number of periods.
    • A period is just a general term for a length of time.
    • Simple interest is rarely used in comparison to compound interest .
    • In compound interest, the interest in one period is also paid on all interest accrued in previous periods.
    • Car loans, mortgages, and student loans all generally have compound interest.

  • Multi-Period Investment

    • Multi-period investments take place over more than one period (usually multiple years).
    • Your total balance will go up each period, because you earn interest each period, but the interest is paid only on the amount you originally borrowed/deposited.
    • The second way of accruing interest is called "compound interest. " In this case, interest is paid at the end of each period based on the balance in the account.
    • Compound interest is named as such because the interest compounds: Interest is paid on interest.
    • The formula for compound interest is.

  • Formulas of Ionic Compounds

    • Two chloride ions were needed in the final compound because calcium had a 2+ charge.
    • Hydroxide is a compound made of oxygen and hydrogen that have been bound together.
    • Cation and Anion Formation - Ionic Compounds Part 2 - YouTube
    • This video shows you how monoatomic ions get their charge, and how to quickly find the charge of ions by looking at the periodic table.
    • Generate the empirical formula of an ionic compound given its molecular constituents.

  • Calculating Present Value

    • Calculating the present value (PV) is a matter of plugging FV, the interest rate, and the number of periods into an equation.
    • If it is compound interest, you can rearrange the compound interest formula to calculate the present value.
    • This is the percentage of interest paid each period.
    • If the problem doesn't say otherwise, it's safe to assume the interest compounds.
    • One area where there is often a mistake is in defining the number of periods and the interest rate.

  • Compounding Frequency

    • Unfortunately, we do not know the time period this interest rate applies to because the time period was omitted.If the 1% is annual, then it is an excellent interest rate for a loan.However, if it is daily, subsequently, this rate is terrible.Borrower took money from a loan shark.For this book, we define all interest rates in annual terms, unless otherwise stated.
    • For example, you deposit $10 in your bank account for 20 years that earns 8% interest (APR), compounded monthly.Consequently, we calculate your savings grow into $49.27 in Equation 12: If your bank compounded your account annually, then you would have $46.61.
    • We can convert any compounding frequency into an APR equivalent interest rate, called the effective annual rate (EFF).From the previous example, we convert the 8% APR interest rate, compounded monthly into an annual rate without compounding, yielding 8.3%.We show the calculation in Equation 13.The EFF is the standard compounding formula removing the years and the present value terms.
    • If you deposited $10 in your bank account for 20 years that earn 8.3% APR with no compounding (or m equals 1), then your savings would grow into $49.27, which is the identical to an interest rate of 8% that is compounded monthly.We calculate this in Equation 14.
    • Banks and financial institutions rarely use continuous compounding to calculate market values of financial securities.Financial analysts and mathematicians use continuous compounding to simplify complex calculations of financial formulas and mathematical models.