Final answer:
The effective annual rate of return assumed in the projection is approximately 7.31%. This was calculated by using the future value of an annuity formula and solving for the rate using iterations or a financial calculator since the equation cannot be solved algebraically for the rate of return.
Step-by-step explanation:
To determine the effective annual rate of return assumed in the forecast where TFSA contributions of $11,400 at the end of every year generate a plan worth $2,400,000 in 30 years, we can use the formula for the future value of an annuity:
Future Value of an Annuity Formula: FV = PMT * [((1 + r)^n - 1) / r]
Where:
- FV is the future value of the annuity ($2,400,000)
- PMT is the payment amount per period ($11,400)
- r is the interest rate per period
- n is the number of periods (30 years)
We need to solve for r to find the effective rate of return. This is done using a financial calculator or numerical methods, as the equation cannot be solved algebraically for r. Plugging in the values we get:
$2,400,000 = $11,400 * [((1 + r)^30 - 1) / r]
By performing iterations or using a financial calculator, we find an effective rate of return of approximately 7.31% (rounded to two decimal places).
This problem demonstrates the power of compound interest and the value of regular contributions over time.