A savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+ :)" . This is n because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) = Pert, and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning. • Why can we write nt nt lim, »0 P(1+) = Plim,0 (1+:)™? n→∞ ∞KU, n n
A savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+ :)" . This is n because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) = Pert, and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning. • Why can we write nt nt lim, »0 P(1+) = Plim,0 (1+:)™? n→∞ ∞KU, n n
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 68SE: An investment account with an annual interest rateof 7 was opened with an initial deposit of 4,000...
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Transcribed Image Text:A savings account with an interest rate r, which is
compounded n times per year, and begins with P as
the principal (initial amount), has the discrete
nt
compounding formula A (t) = P(1+)". This is
n
because we multiply the amount by itself plus a small
amount, determined by the interest rate, and the
account grows each time the compounding occurs.
For continuous compounding, we use the formula
A (t) = Pert , and if we have seen this formula
before, we may not have gotten a satisfactory answer
as to why we use it, other than some vague notion of
"compounding infinity times per year". In this exercise,
we'll use Bernoulli's Rule to find the connection. It
might be helpful to review the "Indeterminate
Powers" section of the video before beginning.
Why can we write
nt
lim,→00 P(1+ )"t
P limn¬∞ (1+)™ ?
n
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