Question

15.a Calculate the FV of (a) an ordinary annuity and (b) an annuity due with payments of $2,000 at the interest rate of 12% per year. (a) $(                     ); (b) $(                            )

15.b Calculate the PV of (a) an ordinary annuity and (b) the annuity due with 5 payments of $2,000 at the interest rate of 12%. (a) $(                       ); (b) $(                      )

(Please hand write and show all steps of the solution no Excel no typing I need to see all steps)

Answer 1

15 a.

Ordinary annuity, payments are made at end of each period

FV = P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P = P[(1+r)ⁿ -1]/r

where, P = 2000
r = 12% = 0.12
n = 5

=> FV = 2000(1.12⁵ - 1] /0.12 = $12705.69

Annuity due, payments are made at starting of each period

FV = P(1+r)ⁿ +....+ P(1+r)² + P(1+r) = P [((1 + r)ⁿ - 1) / r])(1 + r)

where, P = 2000
r = 12% = 0.12
n = 5

=> FV = 2000((1.12)⁵ - 1) / 0.12)(1.12) = $14230.37

12 b.

Ordinary annuity,

PV = P/(1+r) + P/(1+r)² +....+ P/(1+r)ⁿ = P[1- (1+r)^-n]/r

where, P = 2000
r = 12% = 0.12
n = 5

=> PV = 2000(1- 1.12^-5]/0.12 = $7209.55

Annuity Due,

PV = P + P/(1+r) +....+ P/(1+r)^n-1 =P + P[1- (1+r)^-(n-1)]/r

where, P = 2000
r = 12% = 0.12
n = 5

=> PV = 2000 + 2000(1- 1.12^-4]/0.12 = $8074.70