
Мария Петровна положила в банк. 1 500 000 рублей под 7% годовых. Схема начисления процентов
следующая: каждый год банк начисляет проценты на имеющуюся сумму вклада (то есть увеличивает сумму на 7%). По истечению двух лет банк повысил процент с 7% до 10%. Сколько лет должен пролежать вклад, чтобы он увеличился по сравнению с первоначальным на 577993,5 рублей (при условии, что процент изменяться больше не будет)?

Ответы на вопрос

2 год=1 605 000+7%=1 717 350
3год=1 717 350+10%=1 889 085
4 год=1 889 085+10%=2 077 993,5
5 год = 2 077 993,5
Проверка:2 077 993,5- 1 500 000=577993,5



Calculation of Interest for the First Two Years
To calculate the interest for the first two years, we need to determine the interest earned each year based on the initial deposit of 1,500,000 rubles and the interest rate of 7% per annum.
Year 1: - Initial deposit: 1,500,000 rubles - Interest rate: 7% - Interest earned: 1,500,000 * 7/100 = 105,000 rubles
Year 2: - Initial deposit: 1,500,000 rubles + 105,000 rubles (interest earned in Year 1) = 1,605,000 rubles - Interest rate: 7% - Interest earned: 1,605,000 * 7/100 = 112,350 rubles
Change in Interest Rate
After two years, the bank increased the interest rate from 7% to 10%. To calculate the interest earned in subsequent years, we need to consider the new interest rate.
Calculation of Interest for the Remaining Years
To determine the number of years required for the deposit to increase by 577,993.5 rubles, we need to calculate the interest earned in each subsequent year until the desired increase is achieved.
Let's assume the number of years required is 'n'.
Year 3: - Initial deposit: 1,605,000 rubles + 112,350 rubles (interest earned in Year 2) = 1,717,350 rubles - Interest rate: 10% - Interest earned: 1,717,350 * 10/100 = 171,735 rubles
Year 4: - Initial deposit: 1,717,350 rubles + 171,735 rubles (interest earned in Year 3) = 1,889,085 rubles - Interest rate: 10% - Interest earned: 1,889,085 * 10/100 = 188,908.5 rubles
In general, for each subsequent year 'k', the interest earned can be calculated as follows:
Interest earned in Year k: - Initial deposit: (1,889,085 rubles + interest earned in Year k-1) - Interest rate: 10% - Interest earned: (1,889,085 + interest earned in Year k-1) * 10/100
We need to find the value of 'n' for which the deposit increases by 577,993.5 rubles. This can be expressed as:
1,889,085 + (interest earned in Year n-1) = 1,889,085 + 577,993.5
Simplifying the equation, we get:
Interest earned in Year n-1 = 577,993.5
Using the formula for interest earned in Year k, we can calculate the interest earned in Year n-1:
(1,889,085 + interest earned in Year n-2) * 10/100 = 577,993.5
Simplifying further, we have:
188,908.5 + (interest earned in Year n-2) = 577,993.5
Therefore, the deposit needs to be held for 'n-2' years for it to increase by 577,993.5 rubles.
Please note that we need additional information to calculate the exact value of 'n-2'. The interest earned in Year n-2 is required to solve the equation.


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