Question

Начальная сумма составляет 100 р. Ежемесячно она увеличивается на 2,5%. Через сколько месяцев эта сумма возрастет до 115р?

Answer 1

Ответ:

100р. - 100%

100/100=1(р.) - 1%

115/2,5=46 месяцев

Пошаговое объяснение:

Answer 2

Ответ:

Через 6 месяцов

Пошаговое объяснение:

100+2,5%+2,5%+2,5%+2,5%+2,5%+2,5%

Answer 3

Calculation of the Increase in the Initial Amount

To calculate the number of months it will take for the initial amount of 100 rubles to increase to 115 rubles with a monthly increase of 2.5%, we can use the following formula:

Final Amount = Initial Amount × (1 + Monthly Increase Rate)^Number of Months

Let's solve for the number of months:

115 = 100 × (1 + 0.025)^Number of Months

To find the value of the exponent, we can take the logarithm of both sides of the equation:

log(115) = log(100 × (1 + 0.025)^Number of Months)

Using the logarithmic property log(a × b) = log(a) + log(b), we can rewrite the equation as:

log(115) = log(100) + log((1 + 0.025)^Number of Months)

Now, we can isolate the Number of Months:

log((1 + 0.025)^Number of Months) = log(115) - log(100)

Taking the antilogarithm of both sides, we get:

(1 + 0.025)^Number of Months = 115 / 100

Now, we can solve for the Number of Months by taking the logarithm of both sides again:

Number of Months = log(115 / 100) / log(1 + 0.025)

Using a calculator, we can evaluate this expression.

Calculation:

Number of Months = log(115 / 100) / log(1 + 0.025)

Using a calculator, we find that the Number of Months is approximately 7.27 months.

Therefore, it will take approximately 7.27 months for the initial amount of 100 rubles to increase to 115 rubles with a monthly increase of 2.5%.

Please note that the actual number of months may vary slightly due to rounding errors.