Gegeben sind: Höhe der Rate: 1.000 € Prozentsatz: 4% Zeit: 6 Jahre Gesucht ist: Die Höhe des Guthabens nach 6 Jahren 1. Zur Berechnung verwendet man die nachschüssige Rentenformel: ![](data:image/png;base64,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) 2. Einsetzen der Werte in die Formel ergibt: ![](data:image/png;base64,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) 3. Das Ergebnis lautet: ![](data:image/png;base64,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) Lösungsweg Übung 2: Gegeben sind: Höhe der Rate: 5.000 € Prozentsatz: 4,5% Zeit: 18 Jahre Gesucht ist: Die Höhe des Guthabens nach 18 Jahren 1. Zur Berechnung verwendet man die nachschüssige Rentenformel: ![](data:image/png;base64,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) 2. Einsetzen der Werte in die Formel ergibt: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMMAAAAnCAMAAACFdAwMAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOma2OpDbZgAAZgA6ZgBmZmZmZmaQZma2Zrb/kDoAkDo6kDpmkNvbkNv/tmYAtmZmtpCQtrZmttuQtv/btv//25A62/+22////7Zm/9uQ//+2///b5zxBpQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAC7ElEQVRYR+1YC3ObMAyGrFuybknXrqQL3daw8vj//3B6WIAdbESB+K5X3yU2hy19egsnycd4zxoovrzOES/fmtPlp3OSFGm6Oc0h95azTbZ/yzE58/s1IexJfbi5PScV/Fqh5tCddLZgEeo7j/ZAsYQRRrck08FjmuKiZEMifvwZig4KL4NJaAc3G9JFC9SRB5TcZOwt3bLakQzig032KDIk1S4V37L4WQzmw7YosA7zPTsEj77K0DFK9vB22Tz9sWSA45YdBoSwGSwsgzivR4b6APCqHeq5WxaPJHmXC3jV+tKgIfoMlpbBRLRXBoBfH1gGsyy3HAEYD2wheszhcY//PYv2wF5RhibDSG3RtcA7GeofZwD97yfhywmwCeq+eh06FE0Lq78lN92XKB2lJnKrr2gITYVZUQZRoceXKCfxu96yUzzLoKkIK8ogOcjknou8VGxOCB59yiwlAKg45hgJJreGXaXPYGmnoopUdhHg5FYMUsBJccFLzEBYBMjj6XkgHFyUNgOdDNACKIdKiZQ3fSP0buAM5i9f8pLtbQsgrYE7u3TJH8KjOfr7OMVxiziZdMR0kiSkNXDnMbxrvyezVd+DbEQGaQ3ceW2MY/TBBFhimmxzKj31UJK1tAbuzCyaJ79/j4GY+R7jATLC8Vd2v+UOADObVVmlBZAK685GgueXgIvPRBk8jjmkxFxYHyBl+zp+eA8tQEgGOPuNOx0j/rUm4MhVERcQF6HQho1BX2qyzw+jyWgdaxBsNATGbWFa3IvuioWV1sCdyZeOp+e/oo91oHqpImxyIfjogFJfckDYo20BpDVwZw6iWDFNBRvTkan8g98aXQsgrYE7r6B4fVuwAnMtye46wHszoCUVa5/mZiAWNi1f1c2AllicfbqbgTjYtFwHvqqTy5sBLbU4+3Q3A3GwabkO+NLAzYCWWpx9upuBONjUXDU3A2pisTYqbgZiQZvId+LX/0TqV9keuhm4CoAPJktp4D9hw1WihOgp6wAAAABJRU5ErkJggg==) 3. Das Ergebnis lautet: ![](data:image/png;base64,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) von Sandra, Steffi Quelle: https://www.tfh-wildau.de/baetjer/oldpage/Auf_B1/Prakt/Prakt_B2/Pipiale/Pipiale.htm |