6. The bank issued a loan to citizen $N$ on September 9 in the amount of 200 mln rubles. The repayment date is November 22 of the same year. The interest rate on the loan is $25 \%$ per annum. Determine the amount (in thousands of rubles) that citizen N will have to return to the bank. Assume that there are 365 days in a year, the bank accrues interest daily on the loan amount, and no interest is charged on the days of loan issuance and repayment. (14 points).
# Solution:

Number of days of the loan: September - 21 days, October - 31 days, November - 21 days, i.e., $21+31+21=73$ days. The accrued debt amount is calculated using the formula:

$\boldsymbol{F V}=\boldsymbol{P V} \cdot(\boldsymbol{1}+\boldsymbol{t} \cdot \mathbf{Y}$ ), where $\boldsymbol{F} \boldsymbol{V}$ - the accrued (future - future value) amount of money after a certain period; $\boldsymbol{P} \boldsymbol{V}$ - the initial (present - present value) amount of money, $\boldsymbol{t}$ - the term of the operation in days, $\mathbf{Y}$ - the duration of the year in days, $\boldsymbol{i}$ - the interest rate for the period. We have $t=73, Y=365, i=0.25 F V=200 *(1+73 * 0.25 / 365)=1.05 * 200=210$ thousand rubles.

Answer: 210 thousand rubles.

## Grading Criteria:

1) The number of days of the loan is correctly calculated - 3 points.
2) The correct formula for calculating the debt amount is obtained - 7 points
3) The debt amount is correctly calculated - 4 points. If an arithmetic error is made while using the correct formula for calculating the debt amount, 3 points are given.