Question

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 in 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?

Answer 1

Answer:

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

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

recurrence relation is

,
a2 1.09)a
, .........,
an 1.09)an-I

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

Suppose

,

do- 1000

a 1000(9/100)1000

1000(1 + (9/100))

  

1000 (109/100)

1000 (1.09)

a2 1000(1.09)(9/ 100)(1000)(1.09)

  

1000(1.09) (1(9/100))

1000 (1.09)2

Similarly ,

, .

In general ............,

an 1000(1.09)"

Here ,

$a_{1}$ is the amount after 1^st year,

$a_{n}$ is the amount after n^th year of deposit.

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

After 100 years , the amount in the deposit is

a100 100( 1.09) 100

= $ 552904.0791

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