Question

Find the present value of an annuity of $6000 paid at the end of each 6-month period for 8 years if the interest rate is 4%, compounded semiannually. (Round your answer to the nearest cent.)

Answer 1

present value of annuity = P [1 -(1+r)^(-n)] / r

here,

P = periodical payment =>$6000

r = rate of interest =>4% per annum =>4% *6/12 =>2% for six months =>0.02.

n = number of periods =>8 years * 2 semi annual periods =>16 periods.

now,

present value of annuity = $6000 [ 1 - (1.02)^(-16)]/0.02

=>$6000 * [ 0.2715542]/0.02

=>$6,000*13.57771

=>$81,466.26..........(rounded to nearest cent).

present value of the given annuity = $81,466.26....(rounded to nearest cent)