Final answer:
To calculate each payment of the annuity, one must first determine the future value after the deferral period using the future value of a lump sum formula, and then apply the ordinary annuity formula that considers the number of periods, the interest rate per period, and the calculated future value.
Step-by-step explanation:
To determine the amount of each payment for the described annuity, we need to use the formula for the present value of an ordinary annuity because payments are made at the end of each period. In the given scenario, the annuity has a cash value of $13,500, which will grow at a rate of 7% compounded semi-annually for a deferral period of 7 years before the payments begin. Then, the payments will continue for another 8 years.
To solve this, we first need to calculate the future value of the annuity after the 7-year deferral period using the future value of a lump sum formula.
Once we have the future value, we can then use it to find the payment amount by applying the formula for the present value of an ordinary annuity, which will include the total number of payment periods (16 periods for 8 years semi-annually), the interest rate per period (7% per annum compounded semi-annually, thus 3.5% per period), and the future value that was previously calculated.
It is important to note the effect of compound interest in these calculations. As highlighted, compound interest can significantly increase the amount of money accrued over time, which is crucial for determining the payment amounts.