Вам 27 декабря будет нужна сумма 15 тыс. руб. Какую сумму 10 июня этого же года Вы должны положить в банк под простую процентную ставку 36% годовых, если в расчете применяется обыкновенный процент с точным числом дней?
Для решения этой задачи необходимо использовать формулу для расчета простых процентов. Формула выглядит следующим образом:
[ S = P(1 + rt) ]
где:
Мы должны определить, сколько времени пройдет от 10 июня до 27 декабря.
Теперь посчитаем количество дней:
Теперь сложим все дни:
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Давайте разберем задачу поэтапно.
Для расчета используем формулу начисления простых процентов:
[ S = P \cdot (1 + r \cdot t) ]
Где:
Общее количество дней: [ 20 + 31 + 31 + 30 + 31 + 30 + 27 = 200 \, \text{дней}. ]
Теперь вычислим ( t ) (в долях года): [ t = \frac{200}{365}. ]
[ 15\,000 = P \cdot \left(1 + 0.36 \cdot \frac{200}{365}\right). ]
Упростим выражение: [ 15\,000 = P \cdot \left(1 + \frac{72}{365}\right). ]
Здесь ( \frac{72}{365} \approx 0.19726 ), тогда: [ 15\,000 = P \cdot (1 + 0.19726), ] [ 15\,000 = P \cdot 1.19726. ]
Теперь найдем ( P ): [ P = \frac{15\,000}{1.19726}. ]
Выполним деление: [ P \approx 12\,525.74 \, \text{руб}. ]
Для того чтобы 27 декабря получить 15 000 рублей, нужно 10 июня положить в банк 12 525.74 рубля под простую процентную ставку 36% годовых.
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