Question

Find the present value of an annuity in perpetuity that makes payments of $70 at the end of year 6, year 12, year 18, year 24, etc. and makes payments of $60 at the end of year 1, year 4, year 7, year 10, etc. and where effective annual interest is i = 7%.

Answer 1

1. Present value of perpetuity $60 = $60 / [(1 + Interest)^6 - 1]

Present value of perpetuity $60 = $60 / [1.07^6 - 1]

Present value of perpetuity $60 = $60 / 0.50073

Present value of perpetuity $60 every six years= $119.82

2. Present value of annuity $60 every 3 years = Amount * (1 + (1/(1 + Interest)^3 - 1))) / (1 + Interest)

Present value of annuity $60 every 3 years = 60 * (1 + (1/(1.07^3 - 1))) / (1.07)

Present value of annuity $60 every 3 years = 60 * 5.4436 / (1.07)

Present value of annuity $60 every 3 years = $305.25

3. Total present value = $119.82 + 305.25 = $425.07