Question

В июле планируется взять кредит в банке на сумму 9 млн рублей на некоторый срок (целое число лет). Условия его возврата таковы: — каждый январь долг возрастает на 25% по сравнению с концом предыдущего года; — с февраля по июнь каждого года необходимо выплатить часть долга; — в июле каждого года долг должен быть на одну и ту же сумму меньше долга на июль предыдущего года. Чему равна общая сумма выплат после полного погашения кредита если наибольший годовой платеж составит 1,25млн.руб?

Answer 1

Долг не может быть погашен, так как 25 процентов от 9 миллионов равно 2,25 миллиона. Процент от долга превышает выплаты и долг постоянно будет расти

Answer 2

Calculation of Total Repayments for the Loan

To calculate the total repayments for the loan, we need to consider the conditions mentioned:

- The debt increases by 25% every January compared to the end of the previous year. - From February to June of each year, a portion of the debt must be paid. - In July of each year, the debt should be reduced by the same amount as the debt in the previous July.

Let's break down the calculation step by step:

1. Calculate the debt at the end of each year: - The debt at the end of the first year (December) is 9 million rubles. - The debt at the end of the second year (December) will be the debt from the previous year (December) plus 25% of that debt. - The debt at the end of the third year (December) will be the debt from the previous year (December) plus 25% of that debt. - And so on, until the debt at the end of the last year (December) is calculated.

2. Calculate the repayments made from February to June of each year: - The repayments for each year from February to June will be a portion of the debt at the end of the previous year (December). - The portion of the debt to be repaid can be calculated by subtracting the debt at the end of the previous year (December) from the debt at the end of the current year (December).

3. Calculate the total repayments: - The total repayments will be the sum of the repayments made from February to June of each year.

Let's perform the calculations based on the given information.

Calculation Steps:

1. Calculate the debt at the end of each year:

- Debt at the end of the first year (December): 9 million rubles. - Debt at the end of the second year (December): 9 million rubles + 25% of 9 million rubles. - Debt at the end of the third year (December): Debt at the end of the second year + 25% of the debt at the end of the second year. - And so on, until the debt at the end of the last year (December) is calculated.

2. Calculate the repayments made from February to June of each year:

- Repayment for the second year (February to June): Debt at the end of the first year (December) - Debt at the end of the second year (December). - Repayment for the third year (February to June): Debt at the end of the second year (December) - Debt at the end of the third year (December). - And so on, until the repayment for the last year (February to June) is calculated.

3. Calculate the total repayments:

- Total repayments = Repayment for the second year + Repayment for the third year + ... + Repayment for the last year.

Let's calculate the total repayments step by step.

Calculation:

1. Calculate the debt at the end of each year:

- Debt at the end of the first year (December): 9 million rubles. - Debt at the end of the second year (December): 9 million rubles + 25% of 9 million rubles = 9 million rubles + 2.25 million rubles = 11.25 million rubles.- Debt at the end of the third year (December): 11.25 million rubles + 25% of 11.25 million rubles = 11.25 million rubles + 2.8125 million rubles = 14.0625 million rubles.- Debt at the end of the fourth year (December): 14.0625 million rubles + 25% of 14.0625 million rubles = 14.0625 million rubles + 3.515625 million rubles = 17.578125 million rubles.- Debt at the end of the fifth year (December): 17.578125 million rubles + 25% of 17.578125 million rubles = 17.578125 million rubles + 4.39453125 million rubles = 21.97265625 million rubles.- Debt at the end of the sixth year (December): 21.97265625 million rubles + 25% of 21.97265625 million rubles = 21.97265625 million rubles + 5.4931640625 million rubles = 27.4658203125 million rubles.- Debt at the end of the seventh year (December): 27.4658203125 million rubles + 25% of 27.4658203125 million rubles = 27.4658203125 million rubles + 6.866455078125 million rubles = 34.332275390625 million rubles.- Debt at the end of the eighth year (December): 34.332275390625 million rubles + 25% of 34.332275390625 million rubles = 34.332275390625 million rubles + 8.58306884765625 million rubles = 42.91534423828125 million rubles.- Debt at the end of the ninth year (December): 42.91534423828125 million rubles + 25% of 42.91534423828125 million rubles = 42.91534423828125 million rubles + 10.728836059570312 million rubles = 53.64418029785156 million rubles.- Debt at the end of the tenth year (December): 53.64418029785156 million rubles + 25% of 53.64418029785156 million rubles = 53.64418029785156 million rubles + 13.41104507446289 million rubles = 67.05522537231445 million rubles. 2. Calculate the repayments made from February to June of each year:

- Repayment for the second year (February to June): Debt at the end of the first year (December) - Debt at the end of the second year (December) = 9 million rubles - 11.25 million rubles = -2.25 million rubles. (Negative value indicates no repayment is made during this period)- Repayment for the third year (February to June): Debt at the end of the second year (December) - Debt at the end of the third year (December) = 11.25 million rubles - 14.0625 million rubles = -2.8125 million rubles. (Negative value indicates no repayment is made during this period)- Repayment for the fourth year (February to June): Debt at the end of the third year (December) - Debt at the end of the fourth year (December) = 14.0625 million rubles - 17.578125 million rubles = -3.515625 million rubles. (Negative value indicates no repayment is made during this period)- Repayment for the fifth year (February to June): Debt at the end of the fourth year (December) - Debt at the end of the fifth year (December) = 17.578125 million rubles - 21.97265625 million rubles = -4.39453125 million rubles. (Negative value indicates no repayment is made during this period)- Repayment for the sixth year (February to June): Debt at the end of the fifth year (December) - Debt at the end of the sixth year (December) = 21.97265625 million rubles - 27.4658203125 million rubles = -5.4931640625 million rubles. (Negative value indicates no repayment is made during this period)- Repayment for the seventh year (February to June): Debt at the end of the sixth year (December) - Debt at the end of the seventh year (December) = 27.4658203125 million rubles - 34.332275390625 million rubles = -6.866455078125 million rubles. (Negative value indicates no repayment is made during this period)- Repayment for the eighth year (February to June): Debt at the end of the seventh year (December) - Debt at the end of the eighth year (December) = 34.332275390625 million rubles - 42.91534423828125 million rubles = -8.58306884765625 million rubles. (Negative value indicates no repayment is made during this period)- Repayment for the ninth year (February to June): Debt at the end of the eighth year (December) - Debt at the end of the ninth year (December) = 42.91534423828125 million rubles - 53.64418029785156 million rubles = -10.728836059570312 million rubles. (Negative value indicates no repayment is made during this period)- Repayment for the tenth year (February to June): Debt at the end of the ninth year (December) - Debt at the end of the tenth year (December) = 53.64418029785156 million rubles - 67.05522537231445 million rubles = -13.41104507446289 million rubles. (Negative value indicates no repayment is made during this period) 3. Calculate the total repayments:

- Total repayments = Repayment for the second year + Repayment for