Final answer:
The interest earned on the annuity after 5 years is approximately $2,159.11, which is about 12.58% of the total balance of $17,159.11.
Step-by-step explanation:
To calculate the future value of an annuity with compounded interest annually, one can use the annuity formula. In this scenario, the student invests $3,000 annually at an interest rate of 7% over 5 years. The future value of the annuity (FVA) can be calculated using the following formula:
FVA = P * [(1 + r)^n - 1] / r
Where:
P = payment amount per period ($3,000)
r = annual interest rate (7% or 0.07)
n = number of periods (5 years)
Plugging in the values, the future value of this annuity is:
FVA = $3,000 * [(1 + 0.07)^5 - 1] / 0.07
Calculating this gives a future value of approximately $17,159.11.
The total amount paid into the annuity is $3,000 * 5 = $15,000. The interest earned can be found by subtracting the total payments from the future value: Interest = FVA - (P*n). This results in approximately $2,159.11 as the interest earned. To determine the percentage of the balance that is interest, divide the interest earned by the total balance and multiply by 100.
Percentage of interest = ($2,159.11 / $17,159.11) * 100 ≈ 12.58%
Thus, about 12.58% of the final balance is from interest earned.