Final answer:
The present value of the annuity payments that Atlas Insurance offers is approximately $78,818.41. This is the maximum amount you should be willing to pay for the annuity based on the required rate of return of 6.5% per annum.
Step-by-step explanation:
To determine the most you should be willing to pay today for an annuity, you need to calculate the present value of the annuity payments. The annuity payments are $1,600 per quarter for 25 years at a required rate of return of 6.5%. This calculation can be done using the present value formula for an ordinary annuity:
PV = P * [(1 - (1 + r)^(-n)) / r]
where:
- PV is the present value of the annuity.
- P is the payment per period, which is $1,600.
- r is the interest rate per period, which is 6.5% per year or 0.065/4 per quarter.
- n is the total number of payments, which is 4 payments per year times 25 years.
Plugging the values into the formula gives:
PV = $1,600 * [(1 - (1 + 0.065/4)^(-4*25)) / (0.065/4)]
After calculating the above expression, you'll find that the present value of the annuity payments comes to approximately $78,818.41. Therefore, the most you should be willing to pay as a lump sum today to buy this annuity is $78,818.41.