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Chapter 4.4, Problem 73E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Compound Interest In Exercises 73 and 74, $3000 is invested in an account at interest rate r, compounded continuously. Find the time required for the amount to (a) double and (b) triple. r = 8.5 % (a) To determine To calculate: The time required so that the deposited amount become double if the amount of$3000 is deposited in an account at the interest rate of 8.5% and the interest is compounded continuously.

Explanation

Given Information:

The amount of $3000 is deposited in an account at the interest rate of 8.5% and the interest is compounded continuously. Formula used: The balance amount after t years when interest at i is compounded continuously is, A=Pert Where, P is the deposited amount, A is the amount after t years, r is the interest rate in decimals and t is the number of years. The inverse property of logarithms for the expression lnex is lnex=x. Calculation: Consider that the amount of$3000 is deposited in an account at the interest rate of 8.5% and the interest is compounded continuously. So,

P=$3000, r=8.5%. Now the amount become double to the deposited amount after t years, then the amount after t years is 2P, that is, A=2P=2($3000)=$6000 The rate of interest compounded continuously is, r=8.5%=8.5100=0.085 Substitute 0.085 for r,$3000 for P and $6000 for A, in A=Pert (b) To determine To calculate: The time required so that the deposit amount become triple if the amount of$3000 is deposited in an account at the interest rate of 8.5% and the interest is compounded continuously.

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