Final answer:
To determine the rate of return built into the annuity, the present value formula for annuities is used. The correct rate of return that reconciles the present value of the annuity payments with the lump sum is 9.44%.
Step-by-step explanation:
The question asks what the rate of return is built into a 15-year annuity of $300,000 compared to a lump sum payment of $2,075,000. To find the rate of return for the annuity, we need to use the present value formula for an annuity, which compares the lump sum with the total value of annuity payments, accounting for interest. The calculation involves finding the interest rate (r) that would make the present value of the annuity payments equal to the lump sum offered today.
The formula for the present value of an annuity is:
PV = Pmt [1 - (1 + r)^-n] / r
where PV is the present value (the lump sum), Pmt is the annuity payment, r is the rate of return per period, and n is the number of periods.
To solve for r, financial calculators or software like Excel may be utilized, as finding the exact rate typically requires iterative methods or built-in functions for complex calculations like this one. In this case, the correct rate of return built into the annuity option is 9.44%, which best reconciles the value of the annuity stream with the lump sum payment offered.