P653 Calculating Annuities Due LO1 Suppose you are going to

P6-53 Calculating Annuities Due [LO1] Suppose you are going to receive $13,000 per year for 8 years. The appropriate interest rate is 11 percent. Requirement 1: (a) What is the present value of the payments if they are in the form of an ordinary annuity? Click to select) (b) What is the present value if the payments are an annuity due? Click to select) v Requirement 2 (a) Suppose you plan to invest the payments for 8 years, what is the future value if the payments are an ordinary annuity? (Click to select) v (b) Suppose you plan to invest the payments for 8 years, what is the future value if the payments are an annuity due? (Click to select)

Solution

Requirement 1:

a). PVA_Ordinary = P x [{1 - (1 + r)^-n} / r]

= $13,000 x [{1 - (1.11)^-8} / 0.11]

= $13,000 x [0.5661 / 0.11] = $13,000 x 5.1461 = $66,899.60

b). PVA_Due = P + P x [{1 - (1 + r)^{-(n - 1)}} / r]

= $13,000 + $13,000 x [{1 - (1.11)^{-(8 - 1)}} / 0.11]

= $13,000 + $13,000 x [0.5183 / 0.11]

= $13,000 + $13,000 x 4.7122

= $13,000 + $61,258.55 = $74,258.55

Requirement 2:

a). FVA_Ordinary = P x [{(1 + r)ⁿ - 1} / r]

= $13,000 x [{1.11⁸ - 1} / 0.11]

= $13,000 x [1.3045 / 0.11] = $13,000 x 11.8594 = $154,172.65

b).  FVA_Due = (1 + r) x P x [{(1 + r)ⁿ - 1} / r]

= (1 + r) x FVA_Ordinary

  = 1.11 x $154,172.65 = $171,131.64