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

Answer:

To find the balance after 40 years, we need to use the formula for continuously compounded interest:

balance = deposit * e^(rate * time)

Plugging in the values, we get:

balance = $6000 * e^(0.05 * 40)

= $6000 * e^2

= $6000 * 7.39

= $44740

So the student will receive $44740.

Answer 2

Answer:

$44,334.34

Step-by-step 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:

$\implies A=6000e^{0.05 \times40}$

$\implies A=6000e^2$

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

$\implies A=44334.33659...$

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