The present value of a 3-year annuity of $100 is $268.46 when the discount rate is 6%. If the first payment is delayed by 2 years instead of 1 year, the present value would be $174.12.
The present value of a 3-year annuity of $100 can be calculated using the formula:
PV = CF1/(1+r) + CF2/(1+r)² + CF3/(1+r)³
where PV is the present value, CF1, CF2, CF3 are the cash flows in each year, and r is the discount rate.
Let's calculate:
PV = 100/(1+0.06) + 100/(1+0.06)² + 100/(1+0.06)³
PV = 100/1.06 + 100/1.1236 + 100/1.191016
PV = 94.340207 + 89.396222 + 84.726206
PV = 268.462635
Therefore, the present value of the annuity is $268.46 (rounded to 2 decimal places).
b. If you have to wait 2 years instead of 1 year for the first payment, the present value can be calculated by adjusting the cash flow for the first year:
PV = 0/1.06 + 100/(1+0.06)² + 100/(1+0.06)³
PV = 0 + 89.396222 + 84.726206
PV = 174.122428
Therefore, the present value of the annuity with a 2-year delay for the first payment is $174.12 (rounded to 2 decimal places).
Complete Question :
a. What is the present value of a 3-year annuity of $100 if the discount rate is 6%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
b. What is the present value of the annuity in (a) if you have to wait 2 years instead of 1 year for the first payment? (Round your intermediate and final answers to 2 decimal places.)