Question

Find the present value of an ordinary annuity with deposits of $9,078 every 6 months for 4 years at 9.6% compounded semiannually. What is the present value? $ (Round to the nearest cent.)

Answer 1

When interest rates are semi-annual, interest rate is divided by 2 and time period is multiplied by 2

Present value of an annuity

= P x [1 – (1 + r) ^ -n] / r

Where,

P = Periodic Payment = $9,078

r = Interest rate per period

= 9.6 / 2 = 4.8% or 0.048 per period ( since semi-annual compounding)

n = Number of periods = 4 x 2 = 8 (since semi-annual compounding )

So, Present Value of annuity

= $9,078 x [ 1 – ( 1.048 ^ -8)] / 0.048

= $9,078 x [ 1 - 0.687242] / 0.048

= $9,078 x 0.312758 / 0.048

= $9,078 x 6.515792

= $ 59,150.4 ( rounded to nearest cent )