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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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Use the equation found in Example 7 to determine the amount of time it would take for your balance to double at an interest rate of 8.75 % .

To determine

To calculate: The time required so that the deposited amount P (in dollars) will become double if the interest rate is 8.75% and the interest is compounded continuously.

Explanation

Given Information:

The amount of P dollars is deposited at the interest rate of 8.75% and the interest is compounded continuously.

Formula used:

The formula to compute the balance amount after t years when interest 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 deposited amount P (in dollars) will become double when the interest is compounded continuously at the rate of 8.75%.

As the amount will become double of the deposited amount after t years, then the amount after t years is 2P, that is,

A=2P.

Simplify the rate as,

r=8.75%=8.75100=0.0875

Substitute 0.0875 for interest rate, P for the amount deposited and 2P for the amount after t years in the formula“A=Pert”as,

2P=Pe(0

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