Concept explainers
Is the time required for a continuously compoundedinvestment to quadruple twice as long as the time required for it to double? Give a reason for your answer and verify your answer algebraically.
Answer to Problem 142E
The time required for a continuously compounded investment to quadruple is twice as long as the time required for it to double.
Explanation of Solution
Concept used:
Continuous compound interest formula-
A = Final amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form.
Calculation:
Let us assume that the principal amount is P and annual interest rate is r.
The double of principal would be 2P.
Upon substituting our given values in continuous compound interest formula, we will get:
The quadruple of principal would be 4P.
Upon comparing both times, we will get:
Therefore, the time required for a continuously compounded investment to quadruple is twice as long as the time required for it to double.
Chapter 3 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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