TIME VALUE OF MONEY : future-value of single-payment with simple-interest
Year 1:  5% of 100.00 + 100.00 = 105.00
Year 2:  5% of 100.00 + 105.00 = 110.00
Year 3:  5% of 100.00 + 110.00 = 115.00
Year 4:  5% of 100.00 + 115.00 = 120.00
Year 5:  5% of 100.00 + 120.00 = 125.00
( PV × i × t ) + PV
= ( 100.00 × 0.05 × 5 ) + 100.00
= 125.00

TIME VALUE OF MONEY : future-value of single-payment with compound-interest
Year 1:  5% of 100.00 + 100.00 = 105.00
Year 2:  5% of 105.00 + 105.00 = 110.25
Year 3:  5% of 110.25 + 110.25 = 115.76
Year 4:  5% of 115.76 + 115.76 = 121.55
Year 5:  5% of 121.55 + 121.55 = 127.63
PV × ( 1 + i )^t
= 100.00 × ( 1 + 0.05 )⁵
= 127.63

TIME VALUE OF MONEY : future-value of uniform-series-payments (Q) with compound-interest
Year 1: 100.00 x ( 1 + 0.05 )^1-1 = 100.00 x 1.000 = 100.00 ,  100.00 = 100.00
Year 2: 100.00 x ( 1 + 0.05 )^2-1 = 100.00 x 1.050 = 105.00 ,  100.00 + 105.00 = 205.00
Year 3: 100.00 x ( 1 + 0.05 )^3-1 = 100.00 x 1.102 = 110.25 ,  100.00 + 105.00 + 110.25 = 315.25
Year 4: 100.00 x ( 1 + 0.05 )^4-1 = 100.00 x 1.158 = 115.76 ,  100.00 + 105.00 + 110.25 + 115.76 = 430.01
Year 5: 100.00 x ( 1 + 0.05 )^5-1 = 100.00 x 1.216 = 121.55 ,  100.00 + 105.00 + 110.25 + 115.76 + 121.55 = 552.56
Q × ∑ ( 1 + i )^t-1
= 100.00 × [ ( 1 + 0.05 )^1-1 + ( 1 + 0.05 )^2-1 + ( 1 + 0.05 )^3-1 + ( 1 + 0.05 )^4-1 + ( 1 + 0.05 )^5-1 ]
= 100.00 × 5.5256
= 552.56
Q × [ [ ( 1 + i )^t - 1 ] ÷ i ]
= 100.00 × [ [ ( 1 + 0.05 )⁵ - 1 ] ÷ 0.05 ]
= 100.00 × 5.5256
= 552.26

TIME VALUE OF MONEY : present-value of single-payment with compound-interest
FV ÷ ( 1 + i )^t
= 127.63 ÷ ( 1 + 0.05 )⁵
= 100.00

TIME VALUE OF MONEY : present-value of uniform-series-payments (Q) with compound-interest
Year 1:  100.00 x ( 1 + 0.05 )^-1 = 100.00 x 0.952 = 95.24 ,  95.24 = 95.24
Year 2:  100.00 x ( 1 + 0.05 )^-2 = 100.00 x 0.907 = 90.70 ,  95.24 + 90.70 = 185.94
Year 3:  100.00 x ( 1 + 0.05 )^-3 = 100.00 x 0.864 = 86.38 ,  95.24 + 90.70 + 86.38 = 272.32
Year 4:  100.00 x ( 1 + 0.05 )^-4 = 100.00 x 0.823 = 82.27 ,  95.24 + 90.70 + 86.38 + 82.27 = 354.59
Year 5:  100.00 x ( 1 + 0.05 )^-5 = 100.00 x 0.784 = 78.35 ,  95.24 + 90.70 + 86.38 + 82.27 + 78.35 = 432.94
Q × ∑ ( 1 + i )^-t
= 100.00 × [ ( 1 + 0.05 )^-1 + ( 1 + 0.05 )^-2 + ( 1 + 0.05 )^-3 + ( 1 + 0.05 )^-4 + ( 1 + 0.05 )^-5 ]
= 100.00 × 4.3295
= 432.95
Q × [ [ 1 - ( 1 + i )^-t ] ÷ i ]
= 100.00 × [ [ 1 - ( 1 + 0.05 )^-5 ] ÷ 0.05 ]
= 100.00 × 4.3295
= 432.95

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