Jims bank account had an initial deposit of dollars.

Compound interest is .

Formula for the amount when the interest is compounded annually  .

Substitute corresponding values in the above formula.

Find the first five terms of the sequence.

For ,  dollars.

For ,  dollars.

For , dollars.

For , dollars.

For , dollars.

(b)

 In this sequence, each term is times the previous term.

Therefore, a recursive formula for this sequence is  with .

Where  is the number of years after the initial deposit.

An explicit formula for this sequences is ,

Where is the number of years after the initial deposit.

(c)

Whenever  the recursive formula is used, the values are rounded to the nearest numbers at each step.

As with an explicit formula, only need to round the final answer.

For very large values of , explicit formula gives a more accurate balance.

(a)

Balance amount for first one year is dollars.

Balance amount for first two years is dollars.

Balance amount for first three years is dollars.

Balance amount for first four years is dollars.

Balance amount for first five years is dollars.

(b)

A recursive formula for the sequence is  with .

An explicit formula for the sequences is .

(c) For very large values of , explicit formula gives a more accurate balance.