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# A person deposits \$1000 in an account that yields 9% ISBN: 9780073383095 37

## Solution for problem 18E Chapter 2.4

Discrete Mathematics and Its Applications | 7th Edition

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Problem 18E

A person deposits \$1000 in an account that yields 9% interest compounded annually.

a) Set up a recurrence relation for the amount in the account at the end of n years.

b) Find an explicit formula for the amount in the account at the end of n years.

c) How much money will the account contain after 100 years?

Step-by-Step Solution:

Problem 18E

A person deposits \$1000 in an account that yields 9% interest compounded annually.

a) Set up a recurrence relation for the amount in the account at the end of n years.

b) Find an explicit formula for the amount in the account at the end of n years.

c) How much money will the account contain after 100 years?

Step 1:

In this problem, we have to set up a recurrence relation and we have to find the explicit formula for the deposit 1000\$ by a person in an account that yields 9% interest compounded annually.

Step 2:

(a): we have to set up a recurrence relation for the amount in the account that yields 9% interest at the end of n years.

Here interest rate 9% in decimal form is 0.09

Now let an represent the amount after n years, then

an = an-1 + 0.09an-1

an = 1.09an-1

Here a0 = 1000.

Problem 18E

A person deposits \$1000 in an account that yields 9% interest compounded annually.

a) Set up a recurrence relation for the amount in the account at the end of n years.

b) Find an explicit formula for the amount in the account at the end of n years.

c) How much money will the account contain after 100 years?

Step 1:

In this problem, we have to set up a recurrence relation and we have to find the explicit formula for the deposit 1000\$ by a person in an account that yields 9% interest compounded annually.

Step 2 of 2

##### ISBN: 9780073383095

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