Question

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A deposit pf $6000 is made in a college savings fund that pays 5.0% interest, compounded continuously. The balance will be given to a student after the money has earned interest for 40 years. How much (in dollars) will the student receive? (Round your answer to the nearest cent.)

Answer 1

$44,334.34

Explanation:

`\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^(rt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}`

Given:

• P = $6000
• r = 5.0% = 0.05
• t = 40 years

Substitute the given values into the continuous compounding formula and solve for A:

`\implies A=6000e^(0.05 *40)`

`\implies A=6000e^2`

`\implies A=6000(7.3890560...)`

`\implies A=44334.33659...`

Therefore, the balance of the account after 40 years will be $44,334.34 (nearest cent).