Interest Problem Problem: A person borrows $100,000 with an annual rate of 6% for a loan period of 20 years. What should the monthly payment be? Let y(t) be the amount owed at time t. We have the following differential equation, where k is the monthly payment. QyQ+SSRlcTFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiU2I0kidEdGJUYuLCZGKyQiIichIiNJImtHRiUhIzciIiI= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5RzYiNiNJInRHRilGKywmRickIiInISIjSSJrR0YpISM3 QyQ+SSNTMUc2Ii1JJ2Rzb2x2ZUdGJTYjNyRJJGVxMUdGJS8tSSJ5R0YlNiMiIiEiJysrNSIiIg== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Ly1JInlHNiI2I0kidEdGJSwmSSJrR0YlIiQrIyomLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJEYnIyIiJCIjXSIiIiwmIicrKzVGNkYpISQrI0Y2RjY= QyQ+SSNmMUc2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiRJI1MxR0YlLUkieUdGJTYjSSJ0R0YlIiIi LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCZJImtHNiIiJCsjKiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkSSJ0R0YkIyIiJCIjXSIiIiwmIicrKzVGMkYjISQrI0YyRjI= QyQ+SSRBMjBHNiItSSVzdWJzRyUqcHJvdGVjdGVkRzYkL0kidEdGJSIjP0kjZjFHRiUiIiI= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCZJImtHNiIiJCsjKiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyMiIiciIiYiIiIsJiInKys1RjBGIyEkKyNGMEYw QyQ+SSJLRzYiLUkmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JC9JJEEyMEdGJSIiIUkia0dGJSIiIg== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCQqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjIyIiJyIiJiIiIiwmISIiRi5GJEYuRjAiJCsm QyQtSSZldmFsZkclKnByb3RlY3RlZEc2I0kiS0c2IiIiIg== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder JCIrMFExYnIhIig= JSFH JSFH Let's plot the amount owed as a function of time. QyQ+SSJnRzYiLUkpc2ltcGxpZnlHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2Iy1JJXN1YnNHRik2JC9JImtHRiVJIktHRiVJI2YxR0YlIiIi LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCQqJiwmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMjIiInIiImISIiLUYmNiMsJEkidEdGKiMiIiQiI10iIiJGNywmRi9GN0YlRjdGLyEnKys1 QyQtSSVwbG90RzYiNiRJImdHRiUvSSJ0R0YlOyIiISIjPyIiIg== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= %; 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 JSFH Question: Whwn will the person only owe $50,000? QyQ+SSJURzYiLUkmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JC9JImdHRiUiJisrJkkidEdGJSIiIg== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LCQtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCYtSSRleHBHRiU2IyMiIiciIiYjIiIiIiIjRjFGMiMiI10iIiQ= QyQtSSZldmFsZkclKnByb3RlY3RlZEc2I0kiVEc2IiIiIg== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder JCIrNyllTkciISIp JSFH