Question

consider a ten‐cash‐flow annuity, with the first $800 cash flow occurring at t = 9 years and the tenth $800 cash flow occurring 18 years from today.

(1) Specifically using ten single‐sum (single‐cash‐flow) equations and a discount rate of 4%/year, calculate the value of this annuity 9 years from now.  

(2) Specifically using a PV‐of‐annuity equation and a discount rate of 4%/year, calculate the value of this same annuity nine years from now.

(3) Specifically using nothing but Excel’s prepackaged PV function and a discount rate of 4%/year, calculate the value of this same annuity 9 years from today.

Answer 1

1]

value of annuity = sum of present values of cash flows

present value of each cash flow = cash flow / (1 + discount rate)n

where n = number of years after which the cash flow occurs

value of annuity = ($800 / (1 + 4%)0) + ($800 / (1 + 4%)1) + ($800 / (1 + 4%)2) + ($800 / (1 + 4%)3) + ................. + ($800 / (1 + 4%)9​​​​​​​)

value of annuity = $6,748.27

2]

PV of annuity due = P + [P * [1 - (1 + r)-(n-1)] / r]

where P = periodic payment. This is $800

r = interest rate per period. This is 4%.

n = number of periods. This is 10.

PV of annuity = $800 + [$800 * [1 - (1 + 4%)-(10-1)] / 4%

PV of annuity = $6,748.27

3]

PV of annuity is calculated using PV function in Excel :

rate = 4%

nper = 10

pmt = -800

fv = 0

type = 1

PV of annuity = $6,748.27