Question

Первоначальный вклад, положенный в банк под 10% годовых, составил 3 млн. рублей. Найдите размер вклада через год при ежеквартальном начислении процентов.

Answer 1

Ответ:

3.3 млн

Пошаговое объяснение:

1 способ:

Пусть S-первоначальный вклад

К- коэффициент увеличения = 1+r/100=1+0.1=1.1

r=3%

размер вклада через год = SK=3*1.1=3.3млн

2 способ:

S+0.1S=3+0.1*3=3.3

Answer 2

Calculation of the Deposit Amount after One Year with Quarterly Interest Accrual

To calculate the size of the deposit after one year with quarterly interest accrual, we can use the formula for compound interest:

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

Where: - A is the final amount of the deposit after one year - P is the initial deposit amount - 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, the initial deposit amount is 3 million rubles, the annual interest rate is 10% (0.10 in decimal form), and interest is compounded quarterly (n = 4). We need to find the final amount after one year (t = 1).

Plugging in the values into the formula, we get:

A = 3,000,000(1 + 0.10/4)^(4*1)

Simplifying the equation, we have:

A = 3,000,000(1 + 0.025)^4

Calculating the values inside the parentheses, we get:

A = 3,000,000(1.025)^4

Using a calculator, we find that (1.025)^4 is approximately 1.103812890625.

Therefore, the final amount of the deposit after one year with quarterly interest accrual is:

A = 3,000,000 * 1.103812890625

Calculating the result, we find that the final amount is approximately 3,311,438.67 rubles.

So, the size of the deposit after one year with quarterly interest accrual would be approximately 3,311,438.67 rubles.

Please note that the above calculation assumes that no additional deposits or withdrawals are made during the one-year period and that the interest rate remains constant.