A person saving for retirement makes an initial deposit of $1,000 to a bank account earning interest at a rate of 3% per year compounded monthly, and each month she adds an additional $200 to the account For each nonnegative integer n, let An be the amount in the account at the end of n months. Find a recurrence relation relating Ak to Ak-1. Use iteration to find an explicit formula for An.

Step-by-step explanation:

(a)

From the given information:

Let An denote the amount in the account at the end of n month

Thus,

=1000

After the first month ends, interest =

=

Additional deposit = $200

Now,

Interest after 2nd month, =

Additional deposit = $200

Thus:

(b)

From above;

Thus;

To continuity...

Thus, we have a geometric term

where:

a = 1 (first term)

r = 1.0025>1 (common ratio)

Thus;

From equation(3)

so, converting firstly the mixed fractions to improper fractions and then "adding".