Applications of Euler's number using continually compounded interest.

ApplicationsEulerCCI.ipynb

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    "# Applications of Euler's Number: Continuously Compounding Interest\n",
    "When interest is compounded continuously, the amount **A** in an account after **t** years is given by the formula $A=Pe^{rt}$, where **P** is the amount invested or borrowed and **r** is the annual interest rate expressed as a decimal.\n",
    "\n",
    "### Example Problems\n",
    "If you invest $500 at an annual interest rate of 10% compounded continuously, calculate the final amount you will have in the account after five years."
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     "text": [
      "You will have $824.36 in your account.\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "def continually_compounded_interest(P, r, t):\n",
    "    return P*(math.e**(r*t))\n",
    "print(\"You will have $%.2f in your account.\" % round(continually_compounded_interest(500, .1, 5), 3))"
   ]
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   "source": [
    "If you invest $2,000 at an annual interest rate of 13% compounded continuously, calculate the final amount you will have in the account after 20 years."
   ]
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     "text": [
      "You will have $26,927.48 in your account.\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "def continually_compounded_interest(P, r, t):\n",
    "    return P*(math.e**(r*t))\n",
    "final = '${:,.2f}'.format(continually_compounded_interest(2000, .13, 20))\n",
    "print(\"You will have %s in your account.\" % final)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you invest $20,000 at an annual interest rate of 1% compounded continuously, calculate the final amount you will have in the account after 20 years."
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
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    {
     "name": "stdout",
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     "text": [
      "You will have $24,428.06 in your account.\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "def continually_compounded_interest(P, r, t):\n",
    "    return P*(math.e**(r*t))\n",
    "final = '${:,.2f}'.format(continually_compounded_interest(20000, .01, 20))\n",
    "print(\"You will have %s in your account.\" % final)"
   ]
  }
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