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(1.12^{5} - 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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