Question

ЕГЭ(17 номер, профиль). 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 за июль предыдущего года. Чему будет равна общая сумма выплат после полного погашения кредита, если НАИМЕНЬШИЙ годовой платеж составит 1,25 млн рублей? Не могу понять, как найти наименьший платеж, если не указано количество лет.

Answer 1

Calculation of Total Repayment Amount

To calculate the total repayment amount after the complete repayment of the loan, we need to determine the number of years for which the loan will be taken. Unfortunately, the number of years is not provided in the question. Therefore, it is not possible to calculate the exact total repayment amount without this information.

However, I can provide you with an example calculation based on a specific number of years. Let's assume that the loan is taken for 5 years. We can then calculate the total repayment amount based on the given conditions.

Example Calculation for 5 Years

Given: - Loan amount: 9 million rubles - Smallest annual payment: 1.25 million rubles

Based on the given conditions, we can break down the repayment process for each year:

1. January: The debt increases by 25% compared to the end of the previous year. 2. February to June: A portion of the debt must be paid. 3. July: The debt should be reduced by the same amount as the debt for the previous July.

Let's calculate the repayment amount for each year:

Year 1: - January: Debt increases by 25%: 9 million rubles + (25% of 9 million rubles) = 11.25 million rubles - February to June: Partial debt payment - July: Debt reduced by the same amount as the debt for the previous July: 11.25 million rubles - (11.25 million rubles - 9 million rubles) = 9 million rubles

Year 2: - January: Debt increases by 25%: 9 million rubles + (25% of 9 million rubles) = 11.25 million rubles - February to June: Partial debt payment - July: Debt reduced by the same amount as the debt for the previous July: 11.25 million rubles - (11.25 million rubles - 9 million rubles) = 9 million rubles

Year 3: - January: Debt increases by 25%: 9 million rubles + (25% of 9 million rubles) = 11.25 million rubles - February to June: Partial debt payment - July: Debt reduced by the same amount as the debt for the previous July: 11.25 million rubles - (11.25 million rubles - 9 million rubles) = 9 million rubles

Year 4: - January: Debt increases by 25%: 9 million rubles + (25% of 9 million rubles) = 11.25 million rubles - February to June: Partial debt payment - July: Debt reduced by the same amount as the debt for the previous July: 11.25 million rubles - (11.25 million rubles - 9 million rubles) = 9 million rubles

Year 5: - January: Debt increases by 25%: 9 million rubles + (25% of 9 million rubles) = 11.25 million rubles - February to June: Partial debt payment - July: Debt reduced by the same amount as the debt for the previous July: 11.25 million rubles - (11.25 million rubles - 9 million rubles) = 9 million rubles

To calculate the total repayment amount, we sum up the annual payments: 9 million rubles + 9 million rubles + 9 million rubles + 9 million rubles + 9 million rubles = 45 million rubles

Please note that this calculation is based on the assumption of a 5-year loan term. The total repayment amount will vary depending on the actual number of years for which the loan is taken.

If you have any further questions, please let me know.