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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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Modeling Compound Interest In Exercises 25-32, complete the table for an account in which interest is compounded continuously.

See Example 3.

InitialInvestment rate Annual Time to Amountafter Amountafter
double 10 years 25 years
32. 2% $2000.00

To determine

To calculate: The principal amount that must be invested at the interest rate 2% compounded continuously, so that $2000.00 will be available in 10 years, also calculate the time it will take for the investment to double and the accumulated amount after 25 years.

Explanation

Given Information:

The provided rate of interest is 2% and amount after 10 years is $2000.00.

Formula used:

The accumulated amount for an initial investment P compounded continuously at an annual rate of interest r is given by the exponential growth model, A=Pert.

Calculation:

Consider the provided rate of interest is 2% and amount after 10 years is $2000.00.

Here, r=2% or r=0.02 and at time t=10, A=2000.00.

Let P the initial investment.

Substitute t=10, r=0.02 and A=2000.00 in the exponential growth model A=Pert,

2000.00=Pe0.02×10P=2000.00e0.02×10P=1637.46

Hence, the initial amount is $1637.46.

Let the investment take t time to double, that is, at time t, A=2×1637.46.

Substitute 2×1637.46 for A in the exponential growth model A=1637.469e0.02t,

2×1637

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