Question

Ника взял кредит 25000 лари из банка, по договорённости через год он должен вернуть 27500 лари, через2 года 30000лари, через 3 года 32500 лари, через 4 года 35000. Какой был взят кредит:простым или сложным? Чему равно процентное начисление?

Answer 1

Ответ:

Кредит был взят сложным , 10% плюсом

Объяснение:

Answer 2

Calculation of Interest on the Loan

To determine whether the loan taken by Nika is simple or compound, we need to calculate the interest earned over the years based on the given repayment amounts.

Let's calculate the interest earned for each year:

- Year 1: Nika borrowed 25,000 lari and is required to repay 27,500 lari. The interest earned is 27,500 - 25,000 = 2,500 lari. - Year 2: Nika borrowed 25,000 lari and is required to repay 30,000 lari. The interest earned is 30,000 - 25,000 = 5,000 lari. - Year 3: Nika borrowed 25,000 lari and is required to repay 32,500 lari. The interest earned is 32,500 - 25,000 = 7,500 lari. - Year 4: Nika borrowed 25,000 lari and is required to repay 35,000 lari. The interest earned is 35,000 - 25,000 = 10,000 lari.

Type of Loan: Simple or Compound

To determine whether the loan is simple or compound, we need to compare the interest earned each year with the initial loan amount.

In a simple interest loan, the interest earned remains constant throughout the loan term and is calculated only on the initial loan amount. If the interest earned each year is the same, it indicates a simple interest loan.

In a compound interest loan, the interest earned is added to the loan balance, and future interest is calculated based on the new balance. If the interest earned increases each year, it indicates a compound interest loan.

Let's compare the interest earned each year with the initial loan amount:

- Year 1: Interest earned = 2,500 lari, which is 10% of the initial loan amount (25,000 lari). - Year 2: Interest earned = 5,000 lari, which is 20% of the initial loan amount (25,000 lari). - Year 3: Interest earned = 7,500 lari, which is 30% of the initial loan amount (25,000 lari). - Year 4: Interest earned = 10,000 lari, which is 40% of the initial loan amount (25,000 lari).

Since the interest earned increases each year, it indicates that the loan taken by Nika is a compound interest loan.

Calculation of Interest Rate

To calculate the interest rate, we can use the formula for compound interest:

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

Where: - A is the final amount (repayment amount) - P is the principal amount (initial loan amount) - r is the annual interest rate (unknown) - n is the number of times interest is compounded per year (assuming it is compounded annually) - t is the number of years

We can rearrange the formula to solve for r:

r = (A/P)^(1/(n*t)) - 1

Let's calculate the interest rate using the repayment amounts and the initial loan amount:

- Year 1: A = 27,500 lari, P = 25,000 lari, n = 1, t = 1 - Year 2: A = 30,000 lari, P = 25,000 lari, n = 1, t = 2 - Year 3: A = 32,500 lari, P = 25,000 lari, n = 1, t = 3 - Year 4: A = 35,000 lari, P = 25,000 lari, n = 1, t = 4

Let's calculate the interest rate for each year:

- Year 1: r = (27,500/25,000)^(1/(1*1)) - 1 = 0.1 or 10% - Year 2: r = (30,000/25,000)^(1/(1*2)) - 1 = 0.2 or 20% - Year 3: r = (32,500/25,000)^(1/(1*3)) - 1 = 0.3 or 30% - Year 4: r = (35,000/25,000)^(1/(1*4)) - 1 = 0.4 or 40%

Therefore, the interest rate for each year is as follows:

- Year 1: 10% - Year 2: 20% - Year 3: 30% - Year 4: 40%

Please note that the above calculations assume that the interest is compounded annually. If the compounding period is different, the interest rate may vary.

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