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# Trust Fund A philanthropist deposits $5000 in a trust fund that pays 7.5% interest, compounded continuously. The balance will be given to the college from which the philanthropist graduated after the money has earned interest for 50 years. How much will the college receive? # Trust Fund A philanthropist deposits$5000 in a trust fund that pays 7.5% interest, compounded continuously. The balance will be given to the college from which the philanthropist graduated after the money has earned interest for 50 years. How much will the college receive?

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Upper level algebra asked 2020-10-23
Trust Fund A philanthropist deposits $5000 in a trust fund that pays 7.5% interest, compounded continuously. The balance will be given to the college from which the philanthropist graduated after the money has earned interest for 50 years. How much will the college receive? ## Answers (1) 2020-10-24 Calculation: Consider the provided data, P =$5000ZSK, $$\displaystyle{r}={7.5}\%{\quad\text{and}\quad}{P}{S}{K}{1}={50}$$ years
Where, P is principal, ris the rate of interest and 1 is time period in years.
For compounded continuously,
$$\displaystyle{A}={P}{e}^{{{r}{t}}}$$
Substitute the value of A, P, r,t,
$$\displaystyle{A}={5000}{e}^{{{0.075}\cdot{50}}}$$
Calculate $$\displaystyle{5000}{e}^{{{0.075}\cdot{50}}}$$ with the help of a calculator,
$212,605.41 The amount received by the college is$212,605.41.

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