Question

Would you prefer to receive an annuity due for $5,000 per year for 8 years or otherwise similar ordinary annuity? Interest rate is 7%. Explain numerically.

Answer 1

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

Present value of annuity due = (1 + 0.07) * 5,000 * [1 - 1 / (1 + 0.07)⁸] / 0.07

Present value of annuity due = 1.07 * 5,000 * [1 - 0.58201] / 0.07

Present value of annuity due = 1.07 * 5,000 * 5.9713

Present value of annuity due = $31,946.455

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

Present value of ordinary annuity due = 5,000 * [1 - 1 / (1 + 0.07)⁸] / 0.07

Present value of ordinary annuity due = 5,000 * [1 - 0.58201] / 0.07

Present value of ordinary annuity due = 5,000 * 5.9713

Present value of ordinary annuity due = $29,586.5

You would prefer annuity due as it has a higher present value