Question

# 15.a Calculate the FV of (a) an ordinary annuity and (b) an annuity due with payments...

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)

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

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