Answer:
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 [tex]Y_{0}[/tex], 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:
[tex]Y_{0}=$20,000[/tex]
[tex]Y_{1}=$20,000*(1+0.06)+$5,000 = $26,200[/tex]
And for each year we calculate the total savings accumulated, using the savings of the previous year as this period's principal:
[tex]Y_{2}=$26,200*(1+0.06)+$5,000 = $32,772[/tex]
[tex]Y_{3}=$32,772*(1+0.06)+$5,000 = $39,738.32[/tex]
[tex]Y_{4}=$39,738.32*(1+0.06)+$5,000 = $47,122.62[/tex]
[tex]Y_{5}=$47,122.62*(1+0.06)+$5,000 = $54,949.98[/tex]
Therefore the answer is $54,949.98.
In general the formula used for each period is the following:
[tex]P_{n} = P_{n-1}*(1+r)+D[/tex]
Where:
[tex]P_{n}[/tex] are the total savings for the current period,
[tex]P_{n-1}[/tex] are the total savings from last period,
[tex]r[/tex] is the interest rate,
[tex]D[/tex] are the monthly deposits made into the savings account.
We further know that [tex]P_{0}=$20,000[/tex].
