How long does it take for money to increase to a factor of seven when compounded continuously at 7% per year? Round the answer to two decimal places.
How long does it take for money to increase to a factor of seven when compounded continuously at 7% per year? Round the answer to two decimal places.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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How long does it take for money to increase to a factor of seven when compounded continuously at 7% per year? Round the answer to two decimal places.
t=_________ years
Expert Solution
Step 1
Under continuous compounding, the relationship between various variables are given as:
A = Pert
where A = accumulated amount
P = amount invested
r = rate annum compounded continuously
t = time in years
Step 2
We have to find the t such that A = 7P; r = 7%
Hence, 7P = Pe7% x t = Pe0.07t
Hence, e0.07t = 7
Take log to the natural base e on both the sides,
0.07t = ln(7)
Hence, t = ln(7) / 0.07 = 27.80 years
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