Problem 10. (6 points)

Artyom is planning to get a consumer loan from a bank in the amount of 65 thousand rubles for a term of 1 year. Which of the following interest calculation options, in your opinion, would be the most beneficial for Artyom in the case where the principal is repaid at the end of the loan term in one payment?

a) a one-time payment at the end of the loan term in the amount of 68,380 rubles (including interest on the loan);

b) 65,000 rubles + 5% per annum, calculated at a simple interest rate at the end of the loan term;

c) 65,000 rubles + 5% per annum, calculated at a compound interest rate at the end of each month;

d) 65,000 rubles + 5% per annum, calculated at a compound interest rate at the end of the loan term;

e) 65,000 rubles + 5% per annum, calculated at a compound interest rate at the end of each quarter;

f) 65,000 rubles + 5% per annum, calculated at a compound interest rate at the end of each half-year.
Answer: $b, 2$.

## Comment:

option a. 68380 rub.

option b. 65000 rub. $\times(1+5 \% / 100 \%)=68250$ rub.

option c. 65000 rub. $\times(1+5 \% / 100 \% / 12)^{12}=68325.52$ rub.

option d. 65000 rub. $\times(1+5 \% / 100 \%)=68250$ rub.

option e. 65000 rub. $\times(1+5 \% / 100 \% / 4)^{4}=68311.45$ rub.

option f. 65000 rub. $\times(1+5 \% / 100 \% / 2)^{2}=68290.63$ rub.