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The accumulated amount in a savings account at any time t is given by A(t) = 7500(1+0
The accumulated amount in a savings account at any time t is given by A(t) = 7500(1+0.032t)^2.
Find the time when the force of interest equals 0.03.
Expert Solution
A(t)= 7500(1+0.032t)^2
Force and interest= d ln A(t)/ dt
= d ln 7500(1+0.032t)^2/ dt
= d (ln 7500+ 2 ln (1+ 0.032 t))/ dt
= 2 d ln (1+ 0.032 t)/ dt
= 2 (0.032)/ (1+ 0.032 t)
force of interest (given)= 0.03
so,
=> 2* (0.032)/ (1+ 0.032 t)= 0.03
=> 0.03* (1+ 0.032 t)= 2* (0.032)
=> 1+ 0.032 t= 2* (0.032)/ 0.03
=> t= 1/ 0.032* ((2* (0.032)/ 0.03)- 1)
= 35.42
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