Smith makes deposits of 100$ at time 0, and X $ at time 3. the fund grows at a force of interest f= (t^2)/100, t>0. The amount of interest earned from time 3 to time 6 is X. Calculate X.

Any help would be really appreciated.

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- Sep 29th 2008, 08:19 AMmathlovetFinancial math- force of interest

**Smith makes deposits of 100$ at time 0, and X $ at time 3. the fund grows at a force of interest f= (t^2)/100, t>0. The amount of interest earned from time 3 to time 6 is X. Calculate X.**

Any help would be really appreciated. - Sep 29th 2008, 08:58 AMTKHunny
Have you considered the basic formulation? You can do it in stages if it is easier to keep track.

$\displaystyle \int_{0}^{3}\frac{t^{2}}{100} \; dt = \frac{9}{100} = 0.09$

$\displaystyle 100 \cdot e^{0.09} = 109.417$

$\displaystyle \int_{3}^{6}\frac{t^{2}}{100} \; dt = \frac{63}{100} = 0.63$

$\displaystyle (109.417 + X) \cdot e^{0.63} = (109.417 + X) + X$

Solve for X.

Note: You may wish to eliminate some rounding. There really is no need to use the three decimal places for intermediate results. I get an error of about 0.3¢ due to the unnecessary rounding. The integrals are exact to two decimal places, so that creates no additional rounding problem. - Sep 29th 2008, 12:07 PMTKHunny
Hmpf! Let's see you do the next one. Only one for free.