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As the number of compounding periods tends to infinity in continuous compounding, the continuous compound interest rate is referred to as the force of interest . For any continuously differentiable accumulation function a(t), the force of interest, or more generally the logarithmic or continuously compounded return , is a function of time as ...
The return in Japanese yen is the result of compounding the 2% US dollar return on the cash deposit with the 10% return on US dollars against Japanese yen: 1.02 x 1.1 − 1 = 12.2%. In more general terms, the return in a second currency is the result of compounding together the two returns: (+) (+) where
Often described as earning interest on your interest, compounding is done on a schedule — such as daily, monthly or annually. Typically the more frequent the compounding, the more compound ...
If this instantaneous return is received continuously for one period, then the initial value P t-1 will grow to = during that period. See also continuous compounding . Since this analysis did not adjust for the effects of inflation on the purchasing power of P t , RS and RC are referred to as nominal rates of return .
For compound interest loans, the interest is based on the principal and the interest combined. Types of loans that often charge compound interest include: Credit cards that carry a balance
Compound Interest Is Often Fixed. Related to compound interest having more permanence, the gains from compound interest are often based on a fixed rate, whereas compound returns are often variable.
For continuous compounding, 69 gives accurate results for any rate, since ln(2) is about 69.3%; see derivation below. Since daily compounding is close enough to continuous compounding, for most purposes 69, 69.3 or 70 are better than 72 for daily compounding. For lower annual rates than those above, 69.3 would also be more accurate than 72. [3]
For short-term CDs of under 12 months, the APY is often very close to the stated interest rate because the effect of compounding is negligible over such a short period.