S – кредит (в тыс. рублей) сроком на 32 месяца под 2% в месяц.
| Месяц |
Начисленные % (тыс. руб) |
Остаток (тыс. руб) |
| 1 |
\(S \cdot \frac{2}{{100}}\) |
\(S — 250\) |
| 2 |
\(\)\(\left( {S — 250} \right) \cdot \frac{2}{{100}}\) |
\(S — 250 — a\) |
| 3 |
\(\)\(\left( {S — 250 — a} \right) \cdot \frac{2}{{100}}\) |
\(S — 250 — 2a\) |
| … |
… |
… |
| 31 |
\(\)\(\left( {S — 250 — 29a} \right) \cdot \frac{2}{{100}}\) |
\(S — 250 — 30a = 250\) |
| 32 |
\(\)\(\left( {S — 250 — 30a} \right) \cdot \frac{2}{{100}}\) |
0 |
Общая сумма выплат равна сумме кредита (S) плюс начисленные проценты.
\(\left\{ {\begin{array}{*{20}{c}}{S + \frac{2}{{100}} \cdot \left( {S + \frac{{S — 250 + S — 250 — 30a}}{2} \cdot 31} \right) = 2061,5}\\{S — 250 — 30a = 250;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.\,\, \Leftrightarrow \,\,\,\left\{ {\begin{array}{*{20}{c}}{50S + S + \left( {S — 250 — \frac{{30}}{2}a} \right)31 = 103075}\\{30a = S — 500\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.\)
\(51S + 31S — 250 \cdot 31 — \frac{{31}}{2} \cdot 30a = 103075\,\,\,\, \Leftrightarrow \,\,\,\,\,82S — 250 \cdot 31 — \frac{{31}}{2}\left( {S — 500} \right) = 103075\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,82S — 250 \cdot 31 — 15,5S + 250 \cdot 31 = 103075\,\,\,\,\, \Leftrightarrow \,\,\,\,\,66,5S = 103075\,\,\,\,\, \Leftrightarrow \,\,\,\,S = 1550\) тысяч рублей.
Ответ: 1 550.