Question

СРОЧНО Накопления, математика Вы кладёте сегодня 900 рублей в сберегательную книжку с процентной ставкой 2% ежегодно. 1) Сколько денег у вас будет через 14 лет? 2) Сколько потребуется лет, чтобы у вас было 1400 рублей?

Answer 1

Ответ: ниже

Пошаговое объяснение:

(Решаем в обычной процентной ставке, а не сложной, потому что количество лет должно быть целым)

Находим 2% от 900: 900/50=18 рублей

1) 18×14=252 рубля; 900+252=1152 рубля.

2) находим, сколько нужно накопить: 1400-900=500

Находим количество лет: 500/18=27.777(7); округляем в большую сторону, получаем 28 лет.

Answer 2

Calculation of Savings with 2% Annual Interest Rate

To calculate the amount of money you will have in your savings account after a certain number of years, we can use the formula for compound interest:

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

Where: - A is the final amount of money - P is the initial principal (the amount of money you deposit) - r is the annual interest rate (expressed as a decimal) - n is the number of times interest is compounded per year - t is the number of years

Let's calculate the answers to your questions:

1) How much money will you have in 14 years? - Principal (P): 900 rubles - Annual interest rate (r): 2% (0.02 as a decimal) - Compounding frequency (n): 1 (compounded annually) - Number of years (t): 14

Using the formula, we can calculate the final amount (A):

A = 900(1 + 0.02/1)^(1*14)

A = 900(1.02)^14

A ≈ 1124.86 rubles

Therefore, you will have approximately 1124.86 rubles in your savings account after 14 years.

2) How many years will it take for you to have 1400 rubles? - Principal (P): 900 rubles - Annual interest rate (r): 2% (0.02 as a decimal) - Compounding frequency (n): 1 (compounded annually) - Target amount (A): 1400 rubles

We need to solve the equation for t:

1400 = 900(1 + 0.02/1)^(1*t)

1400/900 = (1.02)^t

1.5556 ≈ (1.02)^t

Taking the logarithm of both sides:

log(1.5556) ≈ log((1.02)^t)

t ≈ log(1.5556) / log(1.02)

t ≈ 7.32 years

Therefore, it will take approximately 7.32 years for you to have 1400 rubles in your savings account.

Please note that these calculations are approximate and assume that the interest rate remains constant over the entire period.