Final answer:
The student who deposits $3000 annually at 3% interest compounded annually will have $80,611.10 in the account after 20 years, calculated using the future value of annuity formula.
Step-by-step explanation:
The student's question concerns the calculation of the future value of an annuity when $3000 is deposited annually into an account earning 3% interest compounded annually. To solve this, we use the future value of an annuity formula:
FV = P × 】((1 + r)n - 1) / r【
Where:
FV is the future value of the annuity.
P is the annual deposit ($3000).
r is the annual interest rate (3% or 0.03).
n is the number of years the money is deposited (20).
Now we calculate:
FV = 3000 × 】((1 + 0.03)20 - 1) / 0.03【
Which gives us:
FV = 3000 × 】(1.80611 - 1) / 0.03【
FV = 3000 × 】60.2037【
FV = $80,611.10
So, after 20 years, the student will have $80,611.10 in the account.