Question

Suppose that a person has a savings account with a balance of $50,000. At the end of each year, the account will earn 4% interest, and will then pay the owner $4,000. (a) Show the balance of the account at the end of each of the first five years (rounded to the nearest dollar).

b) Show a recurrence equation for the balance of the account.

c) Find a closed form equation for the future balance of the account. (Hint: this equation will include a summation, Σk=?, ? 1.04k )

Answer 1

ANSWER:

a)

Let P0 be the initial deposited amount and is equal to

Therefore,

similarly,

b)

so, balance in the account after t years will be,

c)

we have,

The above is geometric progression,