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?

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.