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.

  • Calculating the Yield of a Single-Period Investment

    • Nominal APR is simply the interest rate multiplied by the number of payment periods per year.
    • That means that APR=.10 and n=12 (the APR compounds 12 times per year).
    • The Effective Annual Rate is the amount of interest actually accrued per year based on the APR. n is the number of compounding periods of APR per year.
    • Basically, it is a way to account for the time factor in order to get a more accurate number for the actual interest rate.inom is the nominal interest rate.N is the number of compounding periods per year.
    • Differentiate between the different methods of calculating yield of a single period investment

  • 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.

  • Single-Period Investment

    • A period is a general block of time.
    • Usually, a period is one year.
    • The number of periods can be represented as either t or n.
    • Let's go through an example of a single-period investment.
    • Since this is a single-period investment, t (or n) is 1.

  • Calculating Future Value

    • But recall that there are two different formulas for the two different types of interest, simple interest and compound interest .
    • If the problem doesn't specify how the interest is accrued, assume it is compound interest, at least for business problems.
    • This assumes that you don't need to make any payments during the 10 years, and that the interest compounds.
    • In order to get our total number of periods (t), we would multiply 12 months by 10 years, which equals 120 periods.
    • Distinguish between calculating future value with simple interest and with compound interest

  • 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.

  • Calculating and Understanding Average Returns

    • The average ROI is the arithmetic average: divide the total ROI by the number of periods.
    • A stock that appreciates by 3% per year would not actually be worth 15% more over 5 years, because the gains compound.
    • CAGR stands for compound annual growth rate.
    • CAGR, unlike average ROI, does consider compounding returns.
    • CAGR is derived from the compounding interest formula, FV=PV(1+i)t, where PV is the initial value, FV is the future value, i is the interest rate, and t is the number of periods.