Question

Calculate the present value of annuity with payment of $1 at the end of the first year and every two years thereafter. There are total 5 payments. The last payment of $1 is at the end of 9th year. The interest rate is 6% convertible semi-annually.(Write the solution with formulas)

Answer 1

Effective-two year rate, r2 = (1 + 0.06/2)^4 - 1

4 semi-annual periods in two years

r2 = 0.12550881

This formula gives the present value one period before the first payment. Our one period is two-years and the first payment is in one year from now. So, this formula gives present value one year before from today.

n = 5 payments

PMT = 1

Effective annual rate, r1 = (1 + 0.06/2)^2 - 1

r1 = 0.0609

Present value today,

PV0 = PV-1 * (1 + r1)^1

PV0 = 3.5561188557 * (1 + 0.0609)^1

PV0 = $3.772686494