Effective interest rate
Encyclopedia
The effective interest rate, effective annual interest rate, annual equivalent rate (AER) or simply effective rate is the interest rate
on a loan or financial product restated from the nominal interest rate
as an interest rate with annual compound interest
payable in arrears.
It is used to compare the annual interest between loans with different compounding terms (daily, monthly, annually, or other). The effective interest rate differs in two important respects from the annual percentage rate
(APR):
By contrast, the effective APR is used as a legal term, where front-fees and other costs can be included, as defined by local law.
Annual percentage yield
or effective annual yield
is the analogous concept used for savings or investment products, such as a certificate of deposit
. Since any loan is an investment product for the lender, the terms may be used to apply to the same transaction, depending on the point of view.
Effective annual interest or yield may be calculated or applied differently depending on the circumstances, and the definition should be studied carefully. For example, a bank
may refer to the yield on a loan portfolio after expected losses as its effective yield and include income from other fees, meaning that the interest paid by each borrower may differ substantially from the bank's effective yield.
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.
When the frequency of compounding is increased up to infinity the calculation will be:
The yield depends on the frequency of compounding:
The effective interest rate is a special case of the internal rate of return
.
If the monthly interest rate j is known and remains constant throughout the year, the effective annual rate can be calculated as follows:
Interest rate
An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...
on a loan or financial product restated from the nominal interest rate
Nominal interest rate
In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest before adjustment for inflation ; or, for interest rates "as stated" without adjustment for the full effect of compounding...
as an interest rate with annual compound interest
Compound interest
Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...
payable in arrears.
It is used to compare the annual interest between loans with different compounding terms (daily, monthly, annually, or other). The effective interest rate differs in two important respects from the annual percentage rate
Annual percentage rate
The term annual percentage rate , also called nominal APR, and the term effective APR, also called EAR, describe the interest rate for a whole year , 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...
(APR):
- the effective interest rate generally does not incorporate one-time charges such as front-end fees;
- the effective interest rate is (generally) not defined by legal or regulatory authorities (as APR is in many jurisdictions).
By contrast, the effective APR is used as a legal term, where front-fees and other costs can be included, as defined by local law.
Annual percentage yield
Annual Percentage Yield
Annual percentage yield is a normalized representation of an interest rate, based on a compounding period of one year. APY figures allow for a reasonable, single-point comparison of different offerings with varying compounding schedules...
or effective annual yield
Yield (finance)
In finance, the term yield describes the amount in cash that returns to the owners of a security. Normally it does not include the price variations, at the difference of the total return...
is the analogous concept used for savings or investment products, such as a certificate of deposit
Certificate of deposit
A certificate of Deposit is a time deposit, a financial product commonly offered to consumers in the United States by banks, thrift institutions, and credit unions....
. Since any loan is an investment product for the lender, the terms may be used to apply to the same transaction, depending on the point of view.
Effective annual interest or yield may be calculated or applied differently depending on the circumstances, and the definition should be studied carefully. For example, a bank
Bank
A bank is a financial institution that serves as a financial intermediary. The term "bank" may refer to one of several related types of entities:...
may refer to the yield on a loan portfolio after expected losses as its effective yield and include income from other fees, meaning that the interest paid by each borrower may differ substantially from the bank's effective yield.
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.
When the frequency of compounding is increased up to infinity the calculation will be:
The yield depends on the frequency of compounding:
| Nominal Rate | Semi-Annual | Quarterly | Monthly | Daily | Continuous |
|---|---|---|---|---|---|
| 1% | 1.002% | 1.004% | 1.005% | 1.005% | 1.005% |
| 5% | 5.062% | 5.095% | 5.116% | 5.127% | 5.127% |
| 10% | 10.250% | 10.381% | 10.471% | 10.516% | 10.517% |
| 15% | 15.563% | 15.865% | 16.075% | 16.180% | 16.183% |
| 20% | 21.000% | 21.551% | 21.939% | 22.134% | 22.140% |
| 30% | 32.250% | 33.547% | 34.489% | 34.969% | 34.986% |
| 40% | 44.000% | 46.410% | 48.213% | 49.150% | 49.182% |
| 50% | 56.250% | 60.181% | 63.209% | 64.816% | 64.872% |
The effective interest rate is a special case of the internal rate of return
Internal rate of return
The internal rate of return is a rate of return used in capital budgeting to measure and compare the profitability of investments. It is also called the discounted cash flow rate of return or the rate of return . In the context of savings and loans the IRR is also called the effective interest rate...
.
If the monthly interest rate j is known and remains constant throughout the year, the effective annual rate can be calculated as follows:
External links
- http://www.miniwebtool.com/effective-interest-rate-calculator/ Online Effective Interest Rate Calculator