nt The equation A = P + is used when calculating compound interest from investing P dollars at a rate of r% interest being compounded n times per year for t years. a. Consider an investment ofP = $1000, at a rate of 4% (r = 0.04), being invested for %3D t=25 years. Organize in a table (like shown to the right), the amount A of money n A earned, for each of the following compoundings-per-year: annually (n = 1), semi-annually (n = 2), quarterly (n = 4), monthly, %3D %3D daily, every hour, every second. You don't need to show me any 2 work for this, just make the calculations on a calculator and record the result organized in a table. b. What happens to A as the number of compoundings increase? What did you expect to happen? c. Instead of focusing on investments, consider the function y = (1+±) . Construct a table of values (like in part a) for the same values of n. What does y approach? What did you expect? п d. Use L'Hospital's Rule to evaluate lim (1+ n→∞

Question
nt
The equation A = P
+
is used when calculating compound interest from
investing P dollars at a rate of r% interest being compounded n times per year for t
years.
a. Consider an investment ofP = $1000, at a rate of 4% (r = 0.04), being invested for
%3D
t=25 years. Organize in a table (like shown to the right), the amount A of money
n
A
earned, for each of the following compoundings-per-year:
annually (n = 1), semi-annually (n = 2), quarterly (n = 4), monthly,
%3D
%3D
daily, every hour, every second. You don't need to show me any
2
work for this, just make the calculations on a calculator and record
the result organized in a table.
b. What happens to A as the number of compoundings increase? What did you expect
to happen?
c. Instead of focusing on investments, consider the function y = (1+±) . Construct a
table of values (like in part a) for the same values of n. What does y approach? What
did you expect?
п
d. Use L'Hospital's Rule to evaluate lim (1+
n→∞

Image Transcription

nt The equation A = P + is used when calculating compound interest from investing P dollars at a rate of r% interest being compounded n times per year for t years. a. Consider an investment ofP = $1000, at a rate of 4% (r = 0.04), being invested for %3D t=25 years. Organize in a table (like shown to the right), the amount A of money n A earned, for each of the following compoundings-per-year: annually (n = 1), semi-annually (n = 2), quarterly (n = 4), monthly, %3D %3D daily, every hour, every second. You don't need to show me any 2 work for this, just make the calculations on a calculator and record the result organized in a table. b. What happens to A as the number of compoundings increase? What did you expect to happen? c. Instead of focusing on investments, consider the function y = (1+±) . Construct a table of values (like in part a) for the same values of n. What does y approach? What did you expect? п d. Use L'Hospital's Rule to evaluate lim (1+ n→∞

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