Final answer:
To calculate the present value of Christina's annuity payments, we adjust the standard present value formula for an annuity to account for the delayed start of payments. We then discount those payments back to their present value using a discount rate of 7.25%.
Step-by-step explanation:
To determine the present value of Christina's annuity, we need to calculate the value of each $1,200 payment at today's dollar value using the discount rate of 7.25%. The payments start in Year 4 and continue for five years. The formula for the present value of an annuity due (when the first payment is received immediately) is PV = Pmt × [(1 - (1 + r)^-n) / r]. However, since the first payment is not immediate but starts in Year 4, we have to adjust this formula by discounting the result for three years (the time from now until the first payment). This can be done by multiplying the result by (1 + r)^-3.
The modified formula for the present value of Christina's annuity is: Present Value = $1,200 × [(1 - (1 + 0.0725)^-5) / 0.0725] × (1 + 0.0725)^-3. Computing this will give us the present value of the annuity payments.
To give an example with a different set of numbers, think about a two-year bond. The bond was issued for $3,000 at an interest rate of 8%, so it pays $240 in interest each year. To determine the present value at a discount rate of 8% and then at 11%, the formula for the present value of the bond's future cash flows is used. This process demonstrates how to calculate the worth of future payments in present-day terms using the present value formula.