Question

Luis needs an income stream equivalent to $30,000 in today’s dollars at the beginning of each year for
the next 12 years to maintain his standard of living. He assumes that inflation will average 5% over the
long run and that he can earn a 7% compound annual after-tax return on investments. What lump sum
does Luis need to invest today to fund his needs?
A: $322,303.99
B: $325,202.39
C: $355,098.45
D: $392,934.13

Answer 1

Real rate = [(1 + 0.07) / (1 + 0.05)] - 1

Real rate = [1.07 / 1.05] - 1

Real rate = 1.0190476 - 1

Real rate = 0.0190476 or 1.90476%

Present value = (1 + r) * Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value = (1 + 0.0190476) * 30,000 * [1 - 1 / (1 + 0.0190476)¹²] / 0.0190476

Present value = 1.0190476 * 30,000 * 10.6374627

Present value = $325,202.39