An individual deposits an annual bonus into a savings account that pays 6% interest compounded annually. the size of the bonus increases by $5,000 each year, and the initial bonus amount was $20,000. determine how much will be in the account immediately after the fifth deposit.

Immediately after the fifth deposit the individual will have $54,950 in his account.

Explanation:

For each year you have to calculate the total savings that the indivual has in the account.

The first year, denoted by , the individual deposits $20,000 in his account. At the end of the year the interests are accrued on that principal, and the individual also deposits $5,000 more that will bear interests next year. So we have:

And for each year we calculate the total savings accumulated, using the savings of the previous year as this period's principal:

Therefore the answer is $54,949.98.

In general the formula used for each period is the following:

Where:

are the total savings for the current period,

are the total savings from last period,

is the interest rate,

are the monthly deposits made into the savings account.

We further know that .

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