$$ \$ 1000 $$ are deposited in an account with $$ 8.5 \% $$ interest rate, compounded continuously. What is the balance after 5 years? $$ \mathrm{P}=\$ 1000 \quad \mathrm{r}=0.085 \quad \mathrm{t}=5 $$ $$ \mathrm{~F}= $$ Pe $$ ^{r t} \quad \mathrm{~F}=\$[?] $$

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To find the balance after 5 years with continuous compounding, we can use the formula for continuous compounding:

$$ F = Pe^{rt} $$

Given:
- Principal amount $$ P = \$1000 $$
- Interest rate $$ r = 0.085 $$ (8.5%)
- Time $$ t = 5 $$ years

Substitute the given values into the formula:

$$ F = 1000e^{0.085 \times 5} $$

Now, we can calculate the balance after 5 years.
Calculate the value by following steps:
- step0: Calculate:
  $$1000\times \exp \left(0.085\times 5\right)$$
- step1: Multiply the numbers:
  $$1000\times \exp \left(0.425\right)$$
- step2: Calculate:
  $$1000e^{0.425}$$
- step3: Simplify:
  $$1000e^{\frac{17}{40}}$$
- step4: Rewrite the expression:
  $$1000\sqrt[40]{e^{17}}$$
The balance after 5 years with continuous compounding is approximately $1529.59.
The balance after 5 years is approximately \$1,529.59.

are deposited in an account with
interest rate, compounded
continuously.
What is the balance after 5 years?

Pe

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are deposited in an account with interest rate, compounded continuously. What is the balance after 5 years? Pe