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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
#Mai iss 3 years younger than twice the age of her brother . If b represents the age of Mai''s brother .which expression below represents Mai''s age 2-3b 3-2b 2b-3 3b-2 2-3b 3-2b q
So far we have considered differentiation of functions of one independent variable. In many situations, we come across functions with more than one independent variable
in a rhomus ABCD the circum radii of triangles ABD and ACD are 12.5 cm and 25cm respetively then find the area of rhombus.
can you help me? cause im in 7th grade advanced math and tomorrow I have a test tomorrow and I don''t get this
if Sn =3n²+n, find the A.P.
Mathematics Is All Around Us : What is the first thing you do when you get up? Make yourself a nice cup of tea or coffee? If so, then you're using mathematics! Do you agree? Cons
1. His favorite current carrot drink contain 40%. but h eneeds add to 80 quarts wife brought his perfect drink mix.
If the area of a small size pizza is 78.5 in 2 , what size pizza box would required for the small pizza? (Note: Pizza boxes are calculated according to the length of one side.)
Last year Jonathan was 603/4 inches tall. This year he is 651/4 inches tall. How many inches did he grow? Subtract to find outthe difference in heights. You will need to borro
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