S – кредит (в тыс. рублей) сроком на 68 месяцев под 1,5% в месяц.
| Месяц |
Начисленные % (тыс. руб) |
Остаток (тыс. руб) |
| 1 |
\(S \cdot \frac{{1,5}}{{100}}\) |
\(S — a\) |
| 2 |
\(\)\(\left( {S — a} \right) \cdot \frac{{1,5}}{{100}}\) |
\(S — 2a\) |
| … |
… |
… |
| 65 |
\(\)\(\left( {S — 64a} \right) \cdot \frac{{1,5}}{{100}}\) |
\(S — 65a = 900\) |
| 66 |
\(900 \cdot \frac{{1,5}}{{100}}\) |
600 |
| 67 |
\(600 \cdot \frac{{1,5}}{{100}}\) |
300 |
| 68 |
\(\)\(300 \cdot \frac{{1,5}}{{100}}\) |
0 |
Общая сумма выплат равна сумме кредита (S) плюс начисленные проценты.
\(\left\{ {\begin{array}{*{20}{c}}{S + \frac{{1,5}}{{100}} \cdot \left( {\frac{{S + S — 64a}}{2} \cdot 65 + 900 + 600 + 300} \right) = 3748}\\{S — 65a = 900;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.\,\,\, \Leftrightarrow \,\,\,\,\left\{ {\begin{array}{*{20}{c}}{S + \frac{{1,5}}{{100}} \cdot \left( {65S — 32 \cdot 65a + 1800} \right) = 3748}\\{65a = S — 900\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.\)
\(S + \frac{{1,5}}{{100}} \cdot \left( {65S — 32 \cdot S + 32 \cdot 900 + 1800} \right) = 3748\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,S + \frac{{49,5 \cdot S}}{{100}} + 459 = 3748\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,149,5S = 328900\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,S = 2200\) тысяч рублей.
Ответ: 2 200.