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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Compound Interest In Exercises 39-44, complete the table for a savings account in which interest is compounded continuously.

Initial Investment Annual Rate Time to Double Amount After 10 Years

$ 150

_____ 15 yr

______

To determine

To calculate: Annual rate of interest on the savings account and the amount in the account after 10 years.

Explanation

Given:

The initial investment is $150, and the time to double the investment is 15 years.

The interest is compounded annually.

Formula used:

We can use Growth and decay model y=Cekt.

Calculation:

Let us consider the expression:

y=Cekt ……(1)

We have the annual rate, k×100.

As initial investment, C=150 the time required for doubling the investment is t=15.

For doubling the initial investment, y=2C.

By putting the values, y=2C and t=15 in equation (1), we get:

y=Cekt2C=Cek×152=e15kln2=ln(e15k)

By simplifying further,

15k=ln215k=0

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