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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
The logarithmic or continuously compounded return, sometimes called force of interest, is a function of time defined as follows: = ′ () which is the rate of change with time of the natural logarithm of the accumulation function. Conversely:
The 9-person Symbolab team, based in Tel Aviv, will join Course Hero . The platforms will live under independent branding for the near future, according to Andrew Grauer, CEO of Course Hero.
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 ...
For continuous compounding interest, you’ll get more accurate results by using 69.3 instead of 72. The Rule of 72 is an estimate, and 69.3 is harder for mental math than 72, which divides easily ...
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 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]
Source: Investor.gov Compound Interest Calculator. The late starter. If you invested that same $10,000 at age 55, you’d have a much smaller amount to draw from by the age of 65.