Question

31 декабря 2012 года Екатерина взяла в банке 850000 рублей в кредит под 15% годовых. Схема выплаты кредита следующая.: 31 декабря каждого следующего года банк начисляет проценты на оставшуюся сумму долга. (то есть увеличивает долг на 15%),затем Екатерина переводит в банк определенную сумму ежегодного платежа. Какой должна быть сумма ежегодного платежа,чтобы Екатерина выплатила долг тремя равными ежегодными платежами?

Answer 1

1)850000*15:100=127500
2)850000-127500=722500
3)722500*15:100=108375
4)722500-108375=614125
5)614125*5:100=92199
6)614125-92119=522006
7)522006:3=174002-это ежегодный платеж 

Answer 2

Calculation of Annual Payments for the Loan

To determine the amount of the annual payment that Ekaterina should make in order to repay the loan in three equal annual installments, we need to consider the loan amount, the interest rate, and the repayment scheme.

According to the information provided, on December 31, 2012, Ekaterina took a loan of 850,000 rubles from the bank at an annual interest rate of 15%. The repayment scheme involves the bank charging interest on the remaining loan balance on December 31 of each subsequent year, and Ekaterina making an annual payment to the bank.

To calculate the annual payment, we can break down the problem into three steps:

1. Calculate the interest charged by the bank on December 31 of each year. 2. Determine the remaining loan balance after each annual payment. 3. Calculate the annual payment required to repay the loan in three equal installments.

Let's go through each step in detail.

Step 1: Calculate the Interest Charged Each Year

The bank charges interest on the remaining loan balance on December 31 of each year. The interest rate is 15% per year. To calculate the interest charged each year, we multiply the remaining loan balance by the interest rate.

Since we need to calculate the annual payment for three years, we will calculate the interest charged for each of the three years.

Year 1:

The interest charged on December 31, 2013, would be 15% of the remaining loan balance on that date.

Year 2:

The interest charged on December 31, 2014, would be 15% of the remaining loan balance on that date.

Year 3:

The interest charged on December 31, 2015, would be 15% of the remaining loan balance on that date.

Step 2: Determine the Remaining Loan Balance After Each Annual Payment

After each annual payment, the remaining loan balance decreases. To determine the remaining loan balance after each annual payment, we subtract the annual payment amount from the previous remaining loan balance.

Year 1:

The remaining loan balance after the first annual payment on December 31, 2013, would be the initial loan amount minus the annual payment made.

Year 2:

The remaining loan balance after the second annual payment on December 31, 2014, would be the remaining loan balance after the first payment minus the annual payment made.

Year 3:

The remaining loan balance after the third annual payment on December 31, 2015, would be the remaining loan balance after the second payment minus the annual payment made.

Step 3: Calculate the Annual Payment Required

To calculate the annual payment required to repay the loan in three equal installments, we need to divide the total loan amount by three.

Now that we have gone through the steps, let's calculate the annual payment.

Calculation:

Loan amount: 850,000 rubles Interest rate: 15% per year

Step 1: Calculate the Interest Charged Each Year

Year 1: 15% of the remaining loan balance on December 31, 2013 Year 2: 15% of the remaining loan balance on December 31, 2014 Year 3: 15% of the remaining loan balance on December 31, 2015

Step 2: Determine the Remaining Loan Balance After Each Annual Payment

Year 1: Remaining loan balance after the first payment on December 31, 2013 Year 2: Remaining loan balance after the second payment on December 31, 2014 Year 3: Remaining loan balance after the third payment on December 31, 2015

Step 3: Calculate the Annual Payment Required

The annual payment required to repay the loan in three equal installments is the total loan amount divided by three.

Please note that without the specific remaining loan balance after each annual payment, it is not possible to provide an exact calculation of the annual payment amount. However, you can use the information provided to calculate the annual payment by following the steps outlined above.

I hope this helps! Let me know if you have any further questions.