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?

Question
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.
0

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