Question

В банк помещён вклад 64000 рублей под 25% годовых. В конце каждого из первых трёх лет (после начисления процентов) вкладчик дополнительно положил на счёт одну и ту же фиксированную сумму. К концу четвёртого года после начисления процентов оказалось, что он составляет 385 000 рублей. Какую сумму (в рублях) ежегодно добавлял вкладчик?

Answer 1

Расчеты ведем в тысячах рублей.
За 4 года первоначальный вклад вырос в
1) 1,25⁴ = 2,4410625 раз или
2) 64* 1,25⁴ = 156,25 тыс.руб.
Доход от взноса за эти годы
3) 385 - 156,25 = 228,75 тыс.руб.
Взносы лежали разное число лет - от 1-го до 3-х.
4)  а*(1,25³ + 1,25² + 1,25) = 228,75 тыс.руб.
или
4а) а*(1,953125 + 1,5625 + 1,25) = 4,765625*а = 228,75 
или
5) а =228,75 : 4,765625 = 48,000 тыс. руб. - ОТВЕТ 

Answer 2

Calculation of the Annual Additional Deposit

To find out the amount that the depositor added to the account each year, we can work backwards from the final amount of 385,000 rubles at the end of the fourth year.

Let's break down the problem step by step:

1. The initial deposit was 64,000 rubles. 2. The interest rate was 25% per year. 3. At the end of each of the first three years, the depositor added the same fixed amount to the account. 4. By the end of the fourth year, the total amount in the account was 385,000 rubles.

To calculate the annual additional deposit, we need to subtract the interest earned each year from the total amount at the end of the fourth year.

Calculation Steps:

1. Calculate the interest earned each year for the first three years: - Year 1: 64,000 rubles * 0.25 = 16,000 rubles - Year 2: (64,000 rubles + X) * 0.25 = 16,000 rubles - Year 3: (64,000 rubles + X + X) * 0.25 = 16,000 rubles

2. Calculate the total interest earned over the first three years: - Total interest = 16,000 rubles + 16,000 rubles + 16,000 rubles = 48,000 rubles

3. Subtract the total interest earned from the final amount at the end of the fourth year to find the sum of the additional deposits: - Additional deposits = 385,000 rubles - 48,000 rubles = 337,000 rubles

Therefore, the depositor added 337,000 rubles to the account over the course of the first three years.

Answer: The depositor added 337,000 rubles annually.