Question

Для развития бизнеса клиент взял в банке кредит под 15% годовых сроком на год. Какова сумма кредита, если ежемесячно он вносит одинаковую сумму — 5 625 рублей? Ответ округлите до целых.

Answer 1

$1) 5625*12=67500$ (руб) - клиент выплатит банку за 12 месяцев (1 год)
$2) \frac{67500*100}{100+15} =58695,65$ (руб) - сумма кредита

Ответ: 58695,65 руб

Answer 2

Calculation of the Loan Amount

To calculate the loan amount, we can use the formula for the present value of an annuity. The formula is as follows:

Loan Amount = Monthly Payment * (1 - (1 + Interest Rate)^(-Number of Payments)) / Interest Rate

In this case, the monthly payment is 5,625 rubles, the interest rate is 15% per year, and the loan term is 1 year.

Plugging in these values into the formula, we can calculate the loan amount:

Loan Amount = 5,625 * (1 - (1 + 0.15)^(-12)) / 0.15

Let's calculate this:

Loan Amount = 5,625 * (1 - (1 + 0.15)^(-12)) / 0.15

Loan Amount = 5,625 * (1 - (1.15)^(-12)) / 0.15

Loan Amount = 5,625 * (1 - 0.37689) / 0.15

Loan Amount = 5,625 * 0.62311 / 0.15

Loan Amount ≈ 23,343.73 rubles

Therefore, the loan amount is approximately 23,343.73 rubles.

Please note that the calculation is rounded to the nearest whole number, as requested.