Question

3. Find the present value of an annuity-due with payments of $1,800 every 6 months for 8 years at a nominal rate of interest of 5% per annum compounded semian- nually. Answer: $24,086.48

Answer 1

3. Present value of annuity due = A + A*[1- (1+r)^(-(n-1))]/r

here,

A = 1800

r = 5% per annum

=>2.5% per semi annual periods.

=>0.025

n = 8 years *2 semi annual periods

=>16.

n-1=15

present value of annuity due:

=>1800+1800*[1-(1.025)^(-15)]/0.025

=>1800+1800*12.381376

=>1800+22,286.4768

=>$24,086.48.