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Time line of ten years

01/01/2000 to 31/12/2010
│ │
│-------│-------│---------│---------│--------│-------│--------│------│-------│-------------│
│ │
? 1500-----1500----1500-----1500-----1500-----1500----1500---30,000--25,000--10,000


Given
PMT = 1500
n = 7
k = 12 % per annum
P.V = ?
P.V = PMT * 1/k [ 1 – 1/ (1 + k)n ]
= 1500 * 1 / 12 % [ 1 – 1 (1 + 12 %)7 ]
P.V = 1500 * 8.33 [ 1 – 1 / (1.12)7]
= 12500 [ 1 - 1 / 2.21 ]
= 12500 [0.55]
P.V = 6853.89
Given
n = 8 years
k = 12 % per annum
F.V = 30,000
P.V = F.V / (1+k)n
P.V = 30,000 /(1+0.12)8
P.V = 30,000 / 2.48
P.V = 12,116.50
Given
n = 9years
k = 12 % per annum
F.V = 25,000
P.V = F.V / (1+k)n
P.V = 25,000 / (1+0.12)9
P.V = 25,000 / 2.77
P.V = 9,015.25 -

Given
n = 10years
k = 12 % per annum
F.V = 10,000
P.V = F.V / (1+k)n
P.V = 10,000 / (1+0.12)10
P.V = 10,000 / 3.11
P.V = 3,215.43


P.V = 6853.89
P.V = 12,116.50
P.V = 9,015.25
P.V = 3,215.43
P.V = 31,201.07 Answer


Part b
Here we calculate 3th year Present Value

Time line of three years
01/01/2000 to 31/12/2010
│------------│---------│--------- │
0 1 2 3
30,000 80,000

Given
n = 3years
k = 12 % per annum
F.V = 80,000
P.V = F.V / (1+k)n
P.V = 80,000 / (1+0.12)3
P.V = 80,000 / 1.40
P.V = 56,942.42

P.V = 30,000 + 56,942.42
P. V = 86,942.42 answer

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