Question

В июле планируется взять кредить на сумму 69 510 рублей. условие его возврата таковы. каждый январь долг возрастает на 10% по сравнению предыдущего года с февраля по июль необходимо выплатить некоторую часть долга. на сколько рублей больше придется отдать в случае, если кредит будет полностью погашен тремя равными платежами (то есть за три года) по сравнению со случаем, если кредит будет полностью погашен двумя равными платежами ( то есть за два года)?

Answer 1

Пусть ежемесячный платеж равен: х.
Пусть сумма, взятая в кредит, равна: a.
Составим уравнение по условию задачи:

$(1,1a-x)*1,1-x)*1,1-x=0$
$(1,1^2a-1,1x-x)*1,1-x=0$
$1,1^3a-1,1^2x-1,1x-x=0$
$1,1^3a-x(1,1^2+1,1+1)=0$
$1,331a-3,31x=0$
$x=\frac{1,331a}{3,31}$
$3x=\frac{3,993a}{3,31}$

Мы вычислили общий платеж за 3 месяца.

Вычислим общий платеж за 2 месяца:
Пусть ежемесячный платеж равен: y.
Пусть сумма, взятая в кредит, равна: a.
Составим уравнение:

$(1,1a-y)1,1-y=0$
$1,1^2a-1,1y-y=0$
$1,21a-2,1y=0$
$y=\frac{1,21a}{2,1}$
$2y=\frac{2,42a}{2,1}$

$3x-2y=\frac{3,993a}{3,31}-\frac{2,42a}{2,1}$
$a=69510$
$\frac{3,993a}{3,31}-\frac{2,42a}{2,1}=\frac{3,993*69510}{3,31}-\frac{2,42*69510}{2,1}=3,993*21000-2,43*33100$
$=83853-80102=3751$

Ответ:  $3751$

Answer 2

Calculation of Loan Repayment

To calculate the difference in the amount to be repaid when the loan is fully paid off in three equal payments compared to two equal payments, we need to consider the conditions of the loan.

The loan amount is 69,510 rubles, and the repayment conditions are as follows: - The debt increases by 10% every January compared to the previous year. - From February to July, a certain portion of the debt must be paid.

Let's calculate the repayment amount for both scenarios.

Loan Repayment in Three Equal Payments

In this scenario, the loan will be fully paid off in three years, with equal payments made each year.

To calculate the repayment amount, we need to consider the debt increase in January and the payments made from February to July.

1. Debt Increase in January: - In the first year, the debt will increase by 10% compared to the initial loan amount. - In the second year, the debt will increase by 10% compared to the debt at the beginning of the second year. - In the third year, the debt will increase by 10% compared to the debt at the beginning of the third year.

2. Payments from February to July: - Each year, a certain portion of the debt must be paid from February to July.

Let's calculate the repayment amount for each year:

1. First Year: - Debt increase in January: 69,510 * 10% = 6,951 rubles - Payments from February to July: Unknown

2. Second Year: - Debt increase in January: (69,510 + 6,951) * 10% = 7,864.1 rubles - Payments from February to July: Unknown

3. Third Year: - Debt increase in January: (69,510 + 6,951 + 7,864.1) * 10% = 8,781.51 rubles - Payments from February to July: Unknown

To calculate the payments from February to July, we need more information about the specific amounts to be paid each month during this period.

Loan Repayment in Two Equal Payments

In this scenario, the loan will be fully paid off in two years, with equal payments made each year.

To calculate the repayment amount, we need to consider the debt increase in January and the payments made from February to July, similar to the previous scenario.

Let's calculate the repayment amount for each year:

1. First Year: - Debt increase in January: 69,510 * 10% = 6,951 rubles - Payments from February to July: Unknown

2. Second Year: - Debt increase in January: (69,510 + 6,951) * 10% = 7,864.1 rubles - Payments from February to July: Unknown

To calculate the payments from February to July, we need more information about the specific amounts to be paid each month during this period.

Conclusion

To determine the exact difference in the amount to be repaid in the two scenarios, we need additional information about the specific amounts to be paid from February to July in each case. Once we have that information, we can calculate the total repayment amount for each scenario and compare them to find the difference.

Please provide the specific amounts to be paid from February to July in each scenario, and I will be able to calculate the difference in the repayment amount.