A 4-year annuity of eight $9,800 semiannual payments will begin 9 years from now
ID: 2630964 • Letter: A
Question
A 4-year annuity of eight $9,800 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now.
If the discount rate is 7 percent compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
If the discount rate is 7 percent compounded monthly, what is the value three years from now? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
If the discount rate is 7 percent compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
A 4-year annuity of eight $9,800 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now.
Explanation / Answer
monthly rate = 7%/12
EAR semi annual = (1+0.07/12)^6-1 = 3.55%
PV at 9 years from now = 9800 *[1-(1+0.0355)^-8]/0.0355 = 67224.41
PV at 5 years from now = 67224.41/1.0355^8 = 50854.12.ans
b)
PV at 3 years fromnow = 67224.41/1.0355^12 = 44230.90
c)
PV now = 67224.41/1.0355^18 = 35877.75