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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]
is the annual effective interest rate, which is the "true" rate of interest over a year. Thus if the annual interest rate is 12% then i = 0.12 {\displaystyle \,i=0.12} . i ( m ) {\displaystyle \,i^{(m)}} (pronounced "i upper m") is the nominal interest rate convertible m {\displaystyle m} times a year, and is numerically equal to m ...
The force of interest is less than the annual effective interest rate, but more than the annual effective discount rate. It is the reciprocal of the e -folding time. A way of modeling the force of inflation is with Stoodley's formula: δ t = p + s 1 + r s e s t {\displaystyle \delta _{t}=p+{s \over {1+rse^{st}}}} where p , r and s are estimated.
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}
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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