Question

В банк была положена некоторая сумма денег под 10% годовых.Найдите эту сумму,если известно,что через 3 года на счету было 10648 рублей

Answer 1

10 648 - 110%
тогда 9680 - 100%

9680 - 110%
тогда 8800 - 100%

8800 - 110%
тогда 8000 - 100%

было положено 8000 руб

Answer 2

Положили - х р.,
ставка - 10% годов.,

через 1 год стало: 1,1х  (х + 0,1х = 1,1х),
через 2 года: 1,21х  (1,1х + 0,1*1,1х = 1,1х + 0,11х = 1,21х),
через 3 года: 1,331х  (1,21х + 0,1*1,21х = 1,21х + 0,121х = 1,331х),

1,331х = 10648,
х = 10648 : 1,331,
х = 8000 р. - сумма, которую положили в банк

Answer 3

Calculation of the Initial Deposit Amount

To find the initial deposit amount, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where: - A is the final amount after t years - P is the principal amount (initial deposit) - r is the annual interest rate (in decimal form) - n is the number of times interest is compounded per year - t is the number of years

In this case, we know that the final amount after 3 years is 10,648 rubles, the annual interest rate is 10% (0.10 in decimal form), and the interest is compounded annually (n = 1).

Let's substitute the given values into the formula and solve for P:

10,648 = P(1 + 0.10/1)^(1*3)

Simplifying the equation:

10,648 = P(1.10)^3

Taking the cube root of both sides:

∛(10,648) = P(1.10)

∛(10,648) / 1.10 = P

Using a calculator, we find that ∛(10,648) ≈ 22.47.

Therefore, the initial deposit amount is approximately 22.47 rubles.

Please note that the exact value may vary slightly due to rounding.