Question

Максим взял кредит в банке на некоторую сумму сроком на 17 месяцев. Согласно условиям договора Максим возвращает долг ежемесячными платежами. В конце каждого месяца банк увеличивает долг Максима на 6%, а своим платежом заемщик погашает эти проценты и уменьшает сумму долга. Банк подобрал платежи таким образом, чтобы каждый месяц долг уменьшался на одну и ту же величину. На сколько процентов сумма выплат оказалась больше суммы взятой в кредит?

Answer 1

Ответ:

надо сначала выяснить сколько он забрал в кредит и потом решить умножая всё на 6 %

Answer 2

Calculation of Monthly Payments and Debt Reduction

To calculate the percentage by which the total payments exceeded the loan amount, we need to understand the monthly payment structure and the debt reduction pattern.

According to the terms of the contract, Maxim took a loan from the bank for a certain amount for a period of 17 months. The bank increases Maxim's debt by 6% at the end of each month, and Maxim's monthly payment is designed to cover these interest charges and reduce the loan amount by the same amount each month.

Let's assume the loan amount is X.

In the first month, the bank increases Maxim's debt by 6% of X, which is 0.06X. Maxim's monthly payment covers this interest charge and reduces the loan amount by the same amount, so the remaining loan amount after the first month is X - 0.06X = 0.94X.

In the second month, the bank increases Maxim's debt by 6% of the remaining loan amount, which is 0.06 * 0.94X = 0.0564X. Maxim's monthly payment covers this interest charge and reduces the loan amount by the same amount, so the remaining loan amount after the second month is 0.94X - 0.0564X = 0.8836X.

This pattern continues for each subsequent month, with the debt increasing by 6% of the remaining loan amount and Maxim's monthly payment reducing the loan amount by the same percentage.

Calculation of Total Payments

To calculate the total payments made by Maxim over the 17-month period, we need to sum up all the monthly payments.

Since the loan amount is being reduced by the same percentage each month, we can calculate the monthly payment as a percentage of the initial loan amount.

Let's assume the monthly payment percentage is P.

In the first month, Maxim's payment covers the interest charge of 6% of X, which is 0.06X. Therefore, the payment amount in the first month is P * X.

In the second month, the payment amount is P * (X - 0.06X) = P * 0.94X.

This pattern continues for each subsequent month, with the payment amount decreasing by the same percentage.

To calculate the total payments over 17 months, we can sum up the payment amounts for each month.

Total payments = P * X + P * 0.94X + P * 0.8836X + ... + P * (remaining loan amount after 17 months)

Calculation of the Percentage Difference

To calculate the percentage by which the total payments exceeded the loan amount, we need to compare the total payments with the initial loan amount.

Let's assume the total payments over 17 months are Y.

The percentage difference can be calculated using the formula:

Percentage difference = ((Y - X) / X) * 100

By substituting the values of Y and X into the formula, we can calculate the percentage difference.

Please note that the specific values of the loan amount, monthly payment percentage, and remaining loan amount after 17 months are not provided in the question. Without these values, we cannot provide an exact percentage difference. However, you can use the above calculations as a guide to determine the percentage difference based on the specific values in your scenario.