Find the present value on January 1 of an annuity which pays

Find the present value on January 1 of an annuity which pays $2,000 every six months for five years. The first payment is due on the next April 1 and the rate of interest is 9% convertible semiannually.

Solution

FV = 0, N = 10, rate = 9%/2, PMT = 2000

use PV function in Excel with type as 1

value on April 1 = 16,537.58

Value on Jan 1= 16,537.58/1.045^3/6 = 16.177.59