Answer:
The answer is 3. $27,178.
Explanation:
You have to calculate for each year a new principal to be compounded.
Therefore the formula for next period's principal will be:
[tex]P_{n}=P_{n-1}*(1+r)+D[/tex]
Where
[tex]P_{n}[/tex] is the principal for next period,
[tex]P_{n-1}[/tex] is the principal for this period,
r is the interest rate,
D are the deposits made into the savings account at the end of the period. (therefore it will only compound in next period).
The first year the principal will be the graduation gift:
[tex]P_{1}=2500*(1.0775)+3500=6193.75[/tex]
At the end of the second year Jay will have:
[tex]P_{2}=6193.75*(1.0775)+3500=10173.77[/tex]
The third year:
[tex]P_{3}=10173.77*(1.0775)+3500=14462.23[/tex]
The fourth year the amount being deposited changes from $3,500 to $5,000:
[tex]P_{4}=14462.23*(1.0775)+5000=20583.05[/tex]
The fifth year is the last year:
[tex]P_{5}=20583.05*(1.0775)+5000=27178.24[/tex]
The result is rounded to $27,178.
