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Here’s what the letters represent: A is the amount of money in your account. P is your principal balance you invested. R is the annual interest rate expressed as a decimal. N is the number of ...
The formula above can be used for more than calculating the doubling time. If one wants to know the tripling time, for example, replace the constant 2 in the numerator with 3. As another example, if one wants to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.
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 formula is: A = P (1 + r/n) (nt). Don’t get overwhelmed by the formula, though. You can just use a compound interest calculator to figure out how fast your money can grow.
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. Note that the yield increases with the frequency of compounding.
Let be the purchasing power of a dollar at time t (the number of bundles of consumption that can be purchased for $1). Then π t = 1 / ( P L t ) {\displaystyle \pi _{t}=1/(PL_{t})} , where PL t is the price level at t (the dollar price of a bundle of consumption goods).
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%.
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