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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): [1]
The term annual percentage rate of charge (APR), [1] [2] corresponding sometimes to a nominal APR and sometimes to an effective APR (EAPR), [3] 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, [4] etc. It is a finance charge expressed as an annual rate.
This is a reasonable approximation if the compounding is daily. Also, a nominal interest rate and its corresponding APY are very nearly equal when they are small. For example (fixing some large N), a nominal interest rate of 100% would have an APY of approximately 171%, whereas 5% corresponds to 5.12%, and 1% corresponds to 1.005%.
For various interest-accumulation protocols, the accumulation function is as follows (with i denoting the interest rate and d denoting the discount rate): simple interest : a ( t ) = 1 + t ⋅ i {\displaystyle a(t)=1+t\cdot i}
For example, consider a government bond that sells for $95 ('balance' in the bond at the start of period) and pays $100 ('balance' in the bond at the end of period) in a year's time. The discount rate is = % The effective interest rate is calculated using 95 as the base
As an example, consider a $100,000 fixed annuity that credits a 4% annual effective interest rate. The owner receives an interest credit of $4,000. However, in an equity-indexed annuity, the interest credit is linked to the equity markets. For example: Assume the index is the S&P 500, a one-year point-to-point method is used, and the annuity ...
This yields an annualized flat rate of 12%, and an annualized effective or true rate of 19.05%. The true rate can also be calculated by iteration from the amortization schedule, using the compound interest formula. To keep quoted interest rates as low as possible, institutions also often call for one-time origination or administration fees.
The effective rate is calculated in the following way, where r is the effective rate, i the nominal rate (as a decimal, e.g. 12% = 0.12), and n the number of compounding periods per year (for example, 12 for monthly compounding):