**Lecture 25-26. LOAN OPERATIONS**

When repaying a loan with a lump sum payment at the end of the term, the amount of interest from its provision can be determined using the formulas discussed earlier.

**Example…**

The bank issued a loan in the amount of 1 million rubles. for 9 months at a rate of 80% per annum. Determine the repayment amount and the amount of interest for the loan.

*Decision*

According to formula (1.3):

*S* u003d 1,000,000 ( 1 + 0.75 × 0.8 ) u003d 1,600,000 rubles.

The amount of interest received by the bank for the loan will be equal to:

*I* u003d 1,600,000 – 1,000,000 u003d 600,000 rubles.

The amount of interest can also be calculated using the formula (1.2):

*I* u003d 0.75 -0.8-1,000,000 u003d 600,000 rubles.

**Example…**

Credit in the amount of 500 thousand rubles. was taken on 04/12/94 with a maturity of 06/10/94 at a rate of 80% per annum. Determine the amount of interest 16 for a loan with different practices of their calculation.

*Decision*

Under the German practice of accruing interest, the estimated number of days of using the loan will be equal to:

19 +30 + 10 – 1 = 58 days.

The amount of accrued interest according to the formula (1-2) will be:

*I* u003d ( 58/360 ) 0.8 × 500,000 u003d 64,444 rubles.

Under the French practice of calculating interest, the calculated number of days will be equal to:

19 + 31 + 10 – 1 = 59 days.

The amount of accrued interest will be:

*I* u003d ( 59/360) 0.8 × 5500,000 u003d 65,556 rubles.

Under the English practice of calculating interest, their amount will be:

*I* u003d ( 59/365) 0.8 × 500,000 u003d 64,658 rubles.

**Example…**

Under the terms of the loan agreement, the simple interest rate in the first month of using the loan is 80% per annum, and in each subsequent month it increases by 5 percentage points. Determine the amount of interest on a loan in the amount of 800 thousand rubles, taken for 9 months.

*Decision*

By formula (1.6):

*I* = 800,000 (1/12) (0.8 + 0.85 + 0.8 + 0.95 + 1 + 1.05 + + 1.1 + 1.15 + 1.2) =

= 600,000 rubles.

**Example…**

The bank issued a loan of 10 million rubles. for 3 years at a compound annual rate of 60% per annum with repayment in a lump sum. Determine the amount to be repaid and the amount of accrued interest.

*Decision*

According to the formula (1-12), the repaid amount will be:

*S* u003d 10,000,000 (1 + 0.6) 3 u003d 40,960,000 rubles.

The amount of accrued interest will be equal to:

*I* u003d 40,960,000 – 10,000,000 u003d 30,960,000 rubles.

**Example…**

The bank issues long-term loans at a compound rate of 40% per annum. Determine the amount of interest on a loan in the amount of 2 million rubles, repaid in a lump sum payment in 3.5 years.

*Decision*

According to formula (1.14), the repaid amount will be:

*S* u003d 2,000,000 (1 + 0.4) 3 (1 + 0.5 × 0.4) u003d 6,585,600 rubles.

The amount of accrued interest will be equal to:

*I* u003d 6,585,600 – 2,000,000 u003d 4,585,000 rubles.

Similarly, using the previously given formulas, you can determine the term of the loan, the interest rate for the loan, as well as the amount to be issued.

**Example…**

The borrower proposes to take out a loan in the amount of 400 thousand rubles. with repayment in the amount of 1 million rubles. The bank’s interest rate on loans is 90% per annum. Determine how many days you can take a loan (the estimated number of days in a year is 365).

*Decision*

According to formula (1.9), the number of credit days will be equal to:

*d* = days.

**Example…**

The borrower is going to take a bank loan of 1.5 million rubles. with a return in six months of the amount of 2 million rubles. Determine the interest rate on loans, on the basis of which he can choose a bank.

*Decision*

By formula (1.10):

**Example…**

The borrower is going to take a loan for 9 months with a return of 1.5 million rubles. The interest rate on loans is 80% per annum. Determine the loan amount that the borrower can take.

*Decision*

By formula (1.11):

rub.

**Example…**

The borrower intends to take a bank loan on June 25 with repayment on September 1 of the same year in the amount of 1 million rubles. The bank’s rate on loans is 70% per annum. Determine the amount that the borrower can take under the English practice of calculating interest.

*Decision*

The number of days for interest calculation will be equal to:

6 + 31 + 31 + 1 – 1 = 68 days.

According to formula (1.11), the amount that the borrower can take will be:

rub.

**Example…**

The bank issues long-term loans at a compound rate of 45% per annum. Determine for how long a loan of 1 million rubles can be taken if it is supposed to be repaid in a lump sum payment of 2 million rubles.

*Decision*

By formula (1.17):

of the year.

**Example…**

When issuing a loan for 2 years, an amount twice as large must be returned. Determine the annual interest rate used by the bank.

*Decision*

By formula (1.18):

**Example…**

The borrower is going to take out a loan for 2 years with repayment in a lump sum payment of 5 million rubles. The Bank charges interest on long-term loans at a compound rate of 80% per annum. Determine the loan amount that the borrower can take.

*Decision*

By formula (1.19):

rub.

**Example…**

The bank issues a loan for six months in the amount of 1 million rubles. at the expense of credit resources received from the Central Bank at a refinancing rate of 150% per annum. The bank’s interest margin is 3%. Determine the interest rate on the loan for the amounts of expected expenses on it in the amount of 40 and 80 thousand rubles.

*Decision*

The interest rate on the loan will be equal to the sum of the rate for attracting credit resources, the target profit (interest margin) and the cost of servicing the loan, recalculated at the annual interest rate. According to the formula (110), the cost of servicing the loan, with their amount of 40 thousand rubles. in the form of an annual interest rate will be:

and with their sum of 80 thousand rubles. –

Therefore, the values of the interest rate on the loan will be:

*i* = 150 + 3 + 8 = 161%

and

*i* = 150 + 3 + 16 = 169%

respectively.

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