Question

You have a chance to buy an annuity that pays $3,300 at the beginning of each year for 3 years. You could earn 5. 5% on your money in other investments with equal risk. What is the most you should pay for the annuity?.

Answer 1

To determine the maximum price one should pay for the annuity, calculate the present value of immediate payment of $3,300 and add it to the discounted present value of the remaining payments using an interest rate of 5.5% for two years.

Step-by-step explanation:

To determine the most one should pay for the annuity, we calculate the present value of the annuity payments, considering the opportunity cost of the alternative investment which has an equal risk and a return rate of 5.5%. Since the annuity payments are made at the beginning of each period, we must account for the immediate first payment without discounting it and then discount the rest of the payments.

Calculation Steps:

1. 
   
3. Find the present value of the first annuity payment which is $3,300 as it is received immediately.
4. 
   
6. For the remaining payments, use the present value formula for an annuity due since payments are made at the beginning of the period:
   PV = P × [(1 - (1 + r)^-n) / r], where P is the annuity payment, r is the discount rate per period, and n is the number of periods.
7. 
   
9. Since the discount rate is 5.5% (0.055) annually and there are two more payments remaining, input these into the formula to get the present value of these payments.
10. 
    
12. Add the present value of the immediate payment ($3,300) to the present value of the remaining annuity payments to get the total present value of the annuity. This sum represents the amount you should be willing to pay for the annuity.

By following these steps, one ensures they are paying an appropriate price for the annuity considering the alternative investment option available.