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The accumulated amount in a savings account at any time t is given by A(t) = 7500(1+0

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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.

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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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