The effective interest rate (EIR), effective annual interest rate, annual equivalent rate (AER) or simply effective rate is the percentage of interest on a loan or financial product if compound interest accumulates over a year during which no payments are made. It is the compound interest payable annually in arrears, based on the nominal interest rate. It is used to compare the interest rates between loans with different compounding periods.
Depending on the jurisdictional definition, the effective interest rate may be higher than the annual percentage rate (APR), since the APR method reflects the annual total interest charge assuming periodic interest is paid as soon as it accrues and does not take compounding into account. By contrast, the EIR annualizes the periodic rate with compounding by computing the effects of compounding assuming no periodic payment of interest, so that future interest accrues on both the principal and the current interest. EIR is the standard in the European Union and many other countries, while APR is often used in the United States.
Annual percentage yield or effective annual yield is the analogous concept for savings or investments, such as a certificate of deposit. Since a loan by a borrower is an investment for the lender, both terms can apply to the same transaction, depending on the point of view. For a zero-coupon bond such as a US treasury bill, an annual effective discount rate may be specified instead of an effective interest rate, because zero coupon bonds trade at a discount from their face values.
Calculation
The effective interest rate is calculated as if compounded annually. The effective rate is calculated in the following way, where r is the effective annual rate, i the nominal rate, and n the number of compounding periods per year (for example, 12 for monthly compounding):
For example, a nominal interest rate of 6% compounded monthly is equivalent to an effective interest rate of 6.17%. 6% compounded monthly is credited as 6%/12 = 0.005 every month. After one year, the initial capital is increased by the factor (1+0.005)12 ≈ 1.0617. Note that the yield increases with the frequency of compounding.
When the frequency of compounding is increased up to infinity (as for many processes in nature) the calculation simplifies to:
The annual percentage rate (APR) is calculated in the following way, where i is the interest rate for the period and n is the number of periods.
APR = i × n
Effective interest rate (accountancy)
In accountancy, the term effective interest rate is used to describe the rate used to calculate interest expense or income under the effective interest method.[citation needed] This is not the same as the effective annual rate, and is usually stated as an APR rate.
In finance, discounting is a mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date. This transaction is based on the fact that most people prefer current interest to delayed interest because of mortality effects, impatience effects, and salience effects. The discount, or charge, is the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt.
In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of negative interest rates, when the present value will be equal or more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater than tomorrow. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in the form of interest. The initial amount of borrowed funds is less than the total amount of money paid to the lender.
In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum, at a particular rate. It is distinct from a fee which the borrower may pay to the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs.
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed. The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed.
The time value of money is the widely accepted conjecture that there is greater benefit to receiving a sum of money now rather than an identical sum later. It may be seen as an implication of the later-developed concept of time preference.
Compound interest is interest accumulated from a principal sum and previously accumulated interest. It is the result of reinvesting or retaining interest that would otherwise be paid out, or of the accumulation of debts from a borrower.
The yield to maturity (YTM), book yield or redemption yield of a fixed-interest security is an estimate of the total rate of return anticipated to be earned by an investor who buys a bond at a given market price, holds it to maturity, and receives all interest payments and the capital redemption on schedule. It is the (theoretical) internal rate of return : the discount rate at which the present value of all future cash flows from the bond is equal to the current price of the bond. The YTM is often given in terms of Annual Percentage Rate (A.P.R.), but more often market convention is followed. In a number of major markets the convention is to quote annualized yields with semi-annual compounding ; thus, for example, an annual effective yield of 10.25% would be quoted as 10.00%, because 1.05 × 1.05 = 1.1025 and 2 × 5 = 10.
In finance and economics, the nominal interest rate or nominal rate of interest is the rate of interest stated on a loan or investment, without any adjustments or fees.
Future value is the value of an asset at a specific date. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, rate of return; it is the present value multiplied by the accumulation function. The value does not include corrections for inflation or other factors that affect the true value of money in the future. This is used in time value of money calculations.
Bond valuation is the process by which an investor arrives at an estimate of the theoretical fair value, or intrinsic worth, of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.
In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields.
The term annual percentage rate of charge (APR), corresponding sometimes to a nominal APR and sometimes to an effective APR (EAPR), is the interest rate for a whole year (annualized), rather than just a monthly fee/rate, as applied on a loan, mortgage loan, credit card, etc. It is a finance charge expressed as an annual rate. Those terms have formal, legal definitions in some countries or legal jurisdictions, but in the United States:
In finance, a day count convention determines how interest accrues over time for a variety of investments, including bonds, notes, loans, mortgages, medium-term notes, swaps, and forward rate agreements (FRAs). This determines the number of days between two coupon payments, thus calculating the amount transferred on payment dates and also the accrued interest for dates between payments. The day count is also used to quantify periods of time when discounting a cash-flow to its present value. When a security such as a bond is sold between interest payment dates, the seller is eligible to some fraction of the coupon amount.
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows which the investor receives from that investment over a specified time period, such as interest payments, coupons, cash dividends and stock dividends. It may be measured either in absolute terms or as a percentage of the amount invested. The latter is also called the holding period return.
Annual percentage yield (APY) is a normalized representation of an interest rate, based on a compounding period of one year. APY figures allow a reasonable, single-point comparison of different offerings with varying compounding schedules. However, it does not account for the possibility of account fees affecting the net gain. APY generally refers to the rate paid to a depositor by a financial institution, while the analogous annual percentage rate (APR) refers to the rate paid to a financial institution by a borrower.
Mortgage calculators are automated tools that enable users to determine the financial implications of changes in one or more variables in a mortgage financing arrangement. Mortgage calculators are used by consumers to determine monthly repayments, and by mortgage providers to determine the financial suitability of a home loan applicant. Mortgage calculators are frequently on for-profit websites, though the Consumer Financial Protection Bureau has launched its own public mortgage calculator.
In banking and finance, an amortizing loan is a loan where the principal of the loan is paid down over the life of the loan according to an amortization schedule, typically through equal payments.
In finance, mortgage yield is a measure of yield of mortgage-backed bonds. It is also known as cash flow yield. The mortgage yield, or cash flow yield, of a mortgage-backed bond is the monthly compounded discount rate at which net present value of all future cash flows from the bond will be equal to the present price of the bond.
In finance, the weighted-average life (WAL) of an amortizing loan or amortizing bond, also called average life, is the weighted average of the times of the principal repayments: it's the average time until a dollar of principal is repaid.
In investment, an annuity is a series of payments made at equal intervals. Examples of annuities are regular deposits to a savings account, monthly home mortgage payments, monthly insurance payments and pension payments. Annuities can be classified by the frequency of payment dates. The payments (deposits) may be made weekly, monthly, quarterly, yearly, or at any other regular interval of time. Annuities may be calculated by mathematical functions known as "annuity functions".
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