Question

Банк выплачивает 12% годовых. По итогам двух лет клиент получил 72 000 рублей (включая первоначальную сумму и начисленные проценты). Какую сумму он для этого должен был положить на счет?

Answer 1

Пусть искомая сумма -- X.
I год: вложил X --> в конце I года имел (1+12%/100%)*X=1.2X
II год: в банке уже имелась сумма денег (полученная за прошлый год) в размере 1.2X --> в конце II года имел (1+12%/100%)*1.2X=1.2*1.2X=1.44X.
Известно, что по окончанию II года он имел 72000р=>
1.44X=72000
X=50000
Отв.: 50000р

Answer 2

Calculation of the Initial Deposit Amount

To determine the initial deposit amount required to receive a total of 72,000 rubles (including the initial amount and accrued interest) after two years with an annual interest rate of 12%, we can use the formula for compound interest:

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

Where: - A is the final amount (72,000 rubles) - P is the principal amount (initial deposit) - r is the annual interest rate (12% or 0.12) - n is the number of times interest is compounded per year (assuming it is compounded annually, n = 1) - t is the number of years (2 years)

We need to solve for P.

Let's calculate the initial deposit amount step by step:

1. Substitute the given values into the formula: 72,000 = P(1 + 0.12/1)^(1*2)

2. Simplify the equation: 72,000 = P(1.12)^2

3. Divide both sides of the equation by (1.12)^2: P = 72,000 / (1.12)^2

Now, let's calculate the value of P using the formula:

P = 72,000 / (1.12)^2

Using a calculator, we find that the initial deposit amount required is approximately 59,659.09 rubles.

Therefore, the client should have initially deposited around 59,659.09 rubles into the account to receive a total of 72,000 rubles after two years with a 12% annual interest rate.

Please note that the actual calculation may vary slightly depending on the rounding method used.

Calculation Steps:

1. Substitute the given values into the formula: 72,000 = P(1 + 0.12/1)^(1*2)

2. Simplify the equation: 72,000 = P(1.12)^2

3. Divide both sides of the equation by (1.12)^2: P = 72,000 / (1.12)^2

4. Calculate the value of P using the formula: P = 72,000 / (1.12)^2

P ≈ 59,659.09 rubles

Please let me know if there's anything else I can help you with!