a)100×A(0,5)×A(5,10)×A(10,15)A=100×e∫05(0.07−0.005t)dt×e∫510(0.06−0.003t)dt×e0.03×5=100×e0.07t−20.005t2∣05×e0.06t−20.003t2∣510×e0.15=100×e0.35−0.0625×e0.45−0.2925×e0.15=100×e0.2875×e0.1575×e0.15=100×1.3331×1.1706×1.1618=$181.30
at time t=0
A=100×e0.07×5×e0.06×5×e0.073×5A=100×1.4191×1.3499×1.1618A=$222.56
at time t=4
=100×e∫45(0.07−0.005t)dt×e∫510(0.06−0.003t)dt×e0.03×5=100×e0.07t−20.005t2∣45×e0.06t−20.003t2∣510×e0.15=100×e0.2875−0.24×e0.45−0.2925×e0.15=100×e0.0475×e0.1575×e0.15=100×1.0486×1.1706×1.1618=$142.61
at time 6
=100×e∫610(0.06−0.003t)dt×e0.03×5=100×e0.06t−20.003t2∣610×e0.15=100×e0.45−0.27×e0.15=100×e0.18×e0.15=100×1.1972×1.1618=$139.09
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