   Chapter 6.2, Problem 39E

Chapter
Section
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 $1000 12 % _____ _____ To determine To calculate: The total time required to double the initial investment and the amount in the account after 10 years for a savings account in which interest is compounded continuously. Explanation Given: Initial investment -$1000 and annual rate of interest is 12%.

The interest on the savings account is compounded annually.

Formula used:

We can use Growth and decay model y=Cekt

Calculation:

Consider the expression:

y=Cekt …… (1)

We have initial investment, C=1000 and also the annual rate, k=12100.

For doubling the initial investment, y=2C

By putting the above values, k=12100 and y=2C in equation (1), we get:

y=Cekt2C=Ce12100t2=e0.12tln(2)=ln(e0.12t)

By simplifying further,

0

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