Compound interest

(noun)

An interest rate applied to multiple applications of interest during the lifetime of the investment.

Related Terms

Examples of Compound interest in the following topics:

  • Multi-Period Investment

    • They can either accrue simple or compound interest.
    • In compound interest, it is what the balance is that matters.
    • Compound interest is named as such because the interest compounds: Interest is paid on interest.
    • The formula for compound interest is.
    • Compare compound interest to simple interest.

  • Calculating Present Value

    • But first, you must determine whether the type of interest is simple or compound interest.
    • If it is compound interest, you can rearrange the compound interest formula to calculate the present value.
    • If the problem doesn't say otherwise, it's safe to assume the interest compounds.
    • If you happen to be using a program like Excel, the interest is compounded in the PV formula.
    • Distinguish between the formula used for calculating present value with simple interest and the formula used for present value with compound interest

  • 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.
    • You don't earn interest on interest you previously earned.
    • Distinguish between calculating future value with simple interest and with compound interest

  • 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 the case of simple interest the number of periods, t, is multiplied by their interest rate.
    • This makes sense because if you earn $30 of interest in the first period, you also earn $30 of interest in the last period, so the total amount of interest earned is simple t x $30.
    • 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.

  • Calculating Values for Different Durations of Compounding Periods

    • For example, the interest rate could be 12% compounded monthly, but one period is one year.
    • Since interest generally compounds, it is not as simple as multiplying 1% by 12 (1% compounded each month).
    • The EAR can be found through the formula in where i is the nominal interest rate and n is the number of times the interest compounds per year (for continuous compounding, see ).
    • You can think of it as 2% interest accruing every quarter, but since the interest compounds, the amount of interest that actually accrues is slightly more than 8%.
    • The effective annual rate for interest that compounds more than once per year.

  • Comparing Interest Rates

    • Variables, such as compounding, inflation, and the cost of capital must be considered before comparing interest rates.
    • The reason why the nominal interest rate is only part of the story is due to compounding.
    • Since interest compounds, the amount of interest actually accrued may be different than the nominal amount.
    • The EAR is a calculation that account for interest that compounds more than one time per year.
    • It provides an annual interest rate that accounts for compounded interest during the year.

  • Calculating Values for Fractional Time Periods

    • Compounding periods can be any length of time, and the length of the period affects the rate at which interest accrues.
    • The reasoning behind this is that the interest rate in the equation isn't exactly the interest rate that is earned on the money.
    • 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.
    • The last time the account actually accrued interest was at period 6; the interest for period 7 has not yet been paid.
    • The effect of earning 20% annual interest on an initial $1,000 investment at various compounding frequencies.

  • Compounding Frequency

    • Banks and finance companies usually calculate interest payments and deposits monthly.Thus, we adjust the present value formula for different time units.If you refer to Equation 11, we add a new variable, m, the compounding frequency while APR is the interest rate in annual terms.In the monthly case, m equals 12 because a year has 12 months.
    • 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.
    • We expressed the interest rate in APR, so divide it by 12 to obtain the monthly interest rate, yielding 0.8333% in our case.

  • Calculating the Yield of a Single-Period Investment

    • However, since interest compounds, nominal APR is not a very accurate measure of the amount of interest you actually accrue.
    • That means that APR=.10 and n=12 (the APR compounds 12 times per year).
    • Interest usually compounds, so there is a difference between the nominal interest rate (e.g. monthly interest times 12) and the effective interest rate.
    • 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.