Question

What is the present value of $27 received at the end of each year for 2 years? Assume the annual effective rate of interest is 9%. The first payment will be received one year from today (round to the nearest $1).

a: $42

b: $54

c: $88

d: $47

Answer 1

Calculation of Present Value of $ 27 received at the end of each year for 2 years are as follow:

Present Value = Amount Received at the end of year 1/ (1+r%)ⁿ + Amount Received at the end of year 2/ (1+r%)ⁿ

here r% means rate of interest and n refers to the period for which calculation is being made.

= 27/(1+0.09)¹ + 27/(1+0.09)²

  = 24.771 + 22.725

= 47.496

Therefore correct option is (d) i.e. $ 47

The calculation can also be done as follow, as cash flow of both years are same:

Present Value = Amount Receieved * PVAF (r%, n year)

PVAF (r%, n year) is the annuity factor where r% is rate of interest and n refers to no.of years

PVAF(9%, 2 years) = (1+r%)ⁿ-1/(r%*(1+r%)ⁿ)

= (1+0.09)²-1/ (0.09*(1+0.09)²)

= 1.1881-1/(0.09*1.1881)

=0.1881/0.106929

= 1.759111186

Therefore:

Present Value = 27*1.759111186

= $ 47.496