Question

Задание из ЕГЭ под номером 19 или по старому С5. Помогите понять, пожалуйста!31 декабря 2013 года Сергей взял в банке 9 930 000 рублей в кредит под 10% годовых. Схема выплаты кредита следующая: 31 декабря каждого следующего года банк начисляет проценты на оставшуюся сумму долга (то есть увеличивает долг на 10%), затем Сергей переводит в банк определённую сумму ежегодного платежа. Какой должна быть сумма ежегодного платежа, чтобы Сергей выплатил долг тремя равными ежегодными платежами?

Answer 1

Тут для понимания проще назад возвращаться...
х - последний платеж
ежегодный наброс процентов +10% (или *1,1).. значит было до наброса 
х/1,1
предпоследний платеж, опять же х, сумма до него:
х+х/1,1
наброс процентов:
(х+х/1,1)/1,1
и первый его платеж тоже был х, тогда получаем:
$x+ \frac{x+ \frac{x}{1.1} }{1.1} =9 930 000$
1.1²x+1.1x+x=1.1²*9 930 000
$x= \frac{ 1.1^{2} *9930000}{ 1.1^{2} +1.1+1}$
x=$\frac{1.21*9930000}{3.31}$=3630000

Answer 2

Task Understanding

The task is asking for the calculation of the annual payment amount that Sergey should make in order to repay his debt in three equal annual payments. Sergey borrowed 9,930,000 rubles from a bank on December 31, 2013, at an annual interest rate of 10%. The bank calculates interest on the remaining debt each year and Sergey makes an annual payment to the bank.

Solution Approach

To find the annual payment amount, we need to calculate the remaining debt after each payment and distribute it equally over three years. We can use the formula for the present value of an annuity to calculate the annual payment amount.

Solution Steps

1. Calculate the interest for the first year and add it to the initial debt. 2. Calculate the remaining debt after the first payment. 3. Calculate the interest for the second year and add it to the remaining debt. 4. Calculate the remaining debt after the second payment. 5. Calculate the interest for the third year and add it to the remaining debt. 6. Calculate the remaining debt after the third payment. 7. Divide the remaining debt by three to get the annual payment amount.

Let's calculate the annual payment amount step by step.

Step 1: Calculate the interest for the first year

The interest for the first year can be calculated by multiplying the initial debt by the interest rate.

Initial debt: 9,930,000 rubles Interest rate: 10%

Interest for the first year = Initial debt * Interest rate

Interest for the first year = 9,930,000 * 0.10

Step 2: Calculate the remaining debt after the first payment

The remaining debt after the first payment can be calculated by subtracting the interest for the first year from the initial debt.

Remaining debt after the first payment = Initial debt - Interest for the first year

Remaining debt after the first payment = 9,930,000 - (9,930,000 * 0.10)

Step 3: Calculate the interest for the second year

The interest for