Question

P5-18 Calculating deposit needed You put $10,000 in al 3 years, you make another deposit into the same account. Four 7 years after your original $10,000 deposit), the account balanc was the amount of the deposit at the end of year 3? t. Four years later th e is $20,000, w Fürure value of an annuity For each case in the accompanying table, answer the Ps-19 questions that follow. Case Annuity payment Interest rate Annuity length (years) 5 2,500 500 30,000 11,500 6,000 8% 12 20 10 14 30 Calculate the future value of the annuity, assuming that it is (1) An ordinary annuity (2) An annuity due. a. b. Compare your findings in parts a(1) and al2). All else being identical, which ty of annuity-ordinary or annuity due-is preferable? Explain why. 20 Present value of an annuity Consider the following cases.

Answer 1

Solution:

The formula for Future value of ordinary annuity is

FV = P * [ (1+r)^n – 1] / r

Where P = Payment

r = interest rate

n = period

The formula for Future value of annuity due is

FV = (1+r) * P * [ (1+r)^n – 1] / r

Where P = Payment

r = interest rate

n = period

Answers:

Part A )

In the question 5 case are given, assuming the payment is per annum.

Case A:

Ordinary annuity

When P = 2500, n =10 and r =8%

FV = P * [ (1+r)^n – 1] / r = 2500 * [ (1+8%)^10 – 1] / 8% = 2500*1.158925 / 0.08 = 36216.41

Annuity Due:

FV = (1+r) * FV of ordinary annuity = (1+0.08)*36216.41 = 39113.72

Case B:

Ordinary annuity

When P = 500, n =6 and r =12%

FV = P * [ (1+r)^n – 1] / r = 500 * [ (1+12%)^6 – 1] / 12% = 500*0.973823 / 0.12 = 4057.60

Annuity Due:

FV = (1+r) * FV of ordinary annuity = (1+0.12)*4057.60 = 4544.51

Case C:

Ordinary annuity

When P = 30000, n =5 and r =20%

FV = P * [ (1+r)^n – 1] / r = 30,000 * [ (1+20%)^5– 1] / 20% = 30,000*1.48832 / 0.20 = 223,248

Annuity Due:

FV = (1+r) * FV of ordinary annuity = (1+0.20)*223,248 = 267,897.6

Case D:

Ordinary annuity

When P = 11,500, n =8 and r =9%

FV = P * [ (1+r)^n – 1] / r = 11,500 * [ (1+9%)^8 – 1] / 9% = 11,500*0.992563 / 0.09 = 126,827.4

Annuity Due:

FV = (1+r) * FV of ordinary annuity = (1+0.09)*126,827.4 = 138,241.9

Case E:

Ordinary annuity

When P = 6000, n =30 and r =14%

FV = P * [ (1+r)^n – 1] / r = 6000 * [ (1+14%)^30 – 1] / 14% = 6000*49.95016/ 0.14 = 2,140,721

Annuity Due:

FV = (1+r) * FV of ordinary annuity = (1+0.14)* 2,140,721= 2,440,442

Part B)

Annuity due is preferable as it gives higher future value because the interest is paid for one period extra. In annuity due the payment is made at the start of the period