Final answer:
To calculate the maximum price you would pay for an annuity due making annual payments of $4,500 at a market interest rate of 7.8%, use the present value of an annuity due formula. The annuity is priced higher than an ordinary annuity due to receiving payments at the start of each period, and the price adjusts based on current interest rates.
Step-by-step explanation:
To determine the most you would pay for an annuity due with yearly payments of $4,500 given the current market interest rate of 7.8%, you would use the present value formula for an annuity due. This formula considers the timing of the payments and the market interest rate.
Unlike an ordinary annuity, where payments are made at the end of each period, an annuity due consists of payments made at the beginning of each period. Therefore, each payment is discounted one less period compared to an ordinary annuity. This adjustment reflects the higher value of receiving payments sooner rather than later, which is why the annuity due is generally more expensive than an ordinary annuity.
Given that interest rates have changed, it is important to recalculate the present value of the expected future payments. As we learned in the reference material provided, if the market interest rate increases (like from 6% to 9% in the bond scenario), the price of the bond would be expected to be less because you could receive a higher return elsewhere. Similarly, for an annuity, since the current market interest rate is given (7.8%), we use this to find the present value of the annuity due.