compound interest

(noun)

Interest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest.

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.

  • Interest Compounded Continuously

    • Compound interest is accrued when interest is earned not only on principal, but on previously accrued interest: it is interest on interest.
    • In compound interest, interest is accrued on both the principal and on prior interest earned.
    • Compound interest is not linear, but exponential in form.
    • This time we use compound interest instead.
    • You earn the most interest when interest is compounded continuously.

  • 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

  • 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.

  • Properties of Aromatic Compounds

    • Aromatic compounds are ring structures with delocalized $\pi$ electron density that imparts unusual stability.
    • Aromatic compounds are generally nonpolar and immiscible with water.
    • As they are often unreactive, they are useful as solvents for other nonpolar compounds.
    • Aromatic compounds are produced from a variety of sources, including petroleum and coal tar.
    • Aromatic compounds are also interesting because of their presumed role in the origin of life as precursors to nucleotides and amino acids.