Question

If the present value of an ordinary, eight-year annuity is $7,800 and interest rates are 6 percent, what is the present value of the same annuity due? (Round your answer to two decimal places.)

Answer 1

Calculation of Present Value of Annuity Due

Annuity Due is when the cash Flows arises at the beginning of each year.

As per the facts of Question, Present Value of annuity due can be calculated as below:

[where,

PV = Present Value of Annuity Due

CF = Annual Cash Flows

PVAF = Present Value annuity factor

R = Discount rate OR rate of interest = 6%

n= Number of Years =8 years]

CF = $ 1256.0803527 (from Working Note 1)

PVAF(R ,(n-1)years ) = PVAF(6 % ,(8-1)years ) = PVAF(6 % ,7 years )= 5.58238143944 (using Calculator)

Therefore, Present Value of Annuity Due = $ 8268

Working notes:

Calculation of Cash flow (CF) using the  Present Value of Ordinary Annuity

Ordinary Annuity is when the cash Flows arises at the End of each year.

We know That,

PV of Ordinary Annuity= CF x [PVAF (R ,n years )]

PV of Ordinary Annuity = CF x [PVAF (6% ,8 years )]

[PV of Ordinary annnuity = $ 7800 (given)

PVAF (6% ,8 years) = 6.20979381074 (using calculator)]

7800 = CF x 6.20979381074

Therefore, CF = $ 1256.0803527