Question

A 4-year annuity with eight semiannual payments of $11,400 will begin 7 years from now, with the first payment coming 7.5 years from now. If the discount rate is 11 percent compounded monthly, what is the value of this annuity five years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of the annuity $ If the discount rate is 11 percent compounded monthly, what is the value three years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of the annuity $ If the discount rate is 11 percent compounded monthly, what is the current value of the annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of the annuity $

Answer 1

Calculate the value from the perspective of 7 years from now(when first payment comes 7 months for then):

use present value ordinary annuity:

PVoa = PMT[(1-(1/(1+i)ⁿ)) /i ]

because it is a semi-annual pmt/rate use:

i =0.11/2 = 0.055

n = 5yrs of pmts * 2 times per year = 10

PVoa = 11,400 [ (1-(1 / 0.035^10) ) /0.035 ]

= 11,400(0.29108/0.035)

= 11.400(6.831657)

= 94.8089 (value of 7 years from now )

(2) Discount the value (7 years from now) back 2 years to get the value 5 years from now

PV = FV / (1+i)ⁿ

i is still 0.035 , n=2 yrs * 2 times per year = 4

PV = 94.8089/ 1.055⁴

= 76.5313

(3)Keeping track of the timeline

Three years from now will be 6 years away from the eleven years away value,so discount the 11 year value back 6 years (12 semi-annual periods)

discount rate 0.11/2 = 0.055

94.8089/ 0.055¹²

⁼ 1.23736