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If r per annum is the rate at which the principal A is compounded annually, then at the end of k years, the money due is
Q = A (1 + r)k
Suppose compounding is done continuously. i.e. at every instant the principal A is compounded at R per annum. Then,
Q = A eRk
The relationship between R and r is given by the following reasoning:
A (1 + r)k = A eRk
Example
If R = 5.25%, then ln(1 + r) = 5.25% or r = 5.39%
Suppose Rs.100 is being compounded annually at the rate of 10% per annum. What is the future value of Rs.100 at the end of the third year? What is the effective continuously compounded rate of interest? What is the future value of Rs.100 at the end of the third year, using this interest rate?
FV(Rs.100) = 100 x (1.10)3 = 133.1
If r = 0.1, then the continuously compounded rate of interest R is given by
R = ln(1 + 0.1) = 0.0953
FV(Rs.100) = 100 e0.0953 x 3 = 100 x 1.331 = 133.1
Now we need to discuss graphing an equation. The first question which we have to ask is what accurately is a graph of an equation? A graph is the set of all the ordered pairs whos
Fermat's Theorem If f(x) has a relative extrema at x = c and f′(c) exists then x = c is a critical point of f(x). Actually, this will be a critical point that f′(c) =0.
Hi,Is this free?
Critical point of exponential functions and trig functions, Let's see some examples that don't just involve powers of x. Example: find out all the critical points for the
3 1/2 x 1 4/7 x 1 1/3
Q. What is a Mixed Number? Ans. A mixed number is an integer, along with a fractional part, which has the same sign. (Therefore, a mixed number always has two parts.) M
question paper on fractions
I just have a hard time in math in every other class I have an A or B but in math I have a C+ I at least want a B- or B+ or A- or even an A+
If the points for a right angle triangle are XYZ where do I mark the points?
the graph of relation y=f(x) respect to x=2 straight line is symmetrical then which is correct; (option) a) f(x+2)=f(x_2),b)f(2+x)=f(2_x),c)f(x)=f(_x),d)f(x)=_f(_x)
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