Question

If the present value of an ordinary, 4-year annuity is $5,000 and interest rates are 10 percent, what's the present value of the same annuity due?

Answer 1

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

5,000 = Annuity * [1 - 1 / (1 + 0.1)⁴] / 0.1

5,000 = Annuity * [1 - 0.68301] / 0.1

5,000 = Annuity * 3.16987

Annuity = 1,577.354

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

Present value of annuity due = (1 + 0.1) * 1,577.354 * [1 - 1 / (1 + 0.1)⁴] / 0.1

Present value of annuity due = 1.1 * 1,577.354 * [1 - 0.68301] / 0.1

Present value of annuity due = 1.1 * 1,577.354 * 3.16987

Present value of annuity due = $5,500.01