In May $2024$ , Roman Matveevich plans to take out a loan for business development for three years in the amount of $1,600,000$ rubles. Conditions for its return such: Each January debt increases by $25\%$ compared to the end work of the year; -- from February to April of each year it is necessary to pay one fee - press part of the debt; - payments in $2025$ and $2026$ should be equal: -- by May $2027$ , the debt must be repaid in full. It is known that all funds after full repayment of the loan it will be equal to $2,637.5$ thousand rubles. How many thousand rubles is the payment? Roman Matveevich in $2026$ ?

Full solution

Q. In May

2024

, Roman Matveevich plans to take out a loan for business development for three years in the amount of

1,600,000

rubles. Conditions for its return such: Each January debt increases by

25\%

compared to the end work of the year; -- from February to April of each year it is necessary to pay one fee - press part of the debt; - payments in

2025

and

2026

should be equal: -- by May

2027

, the debt must be repaid in full. It is known that all funds after full repayment of the loan it will be equal to

2,637.5

thousand rubles. How many thousand rubles is the payment? Roman Matveevich in

2026

Initial Loan Calculation: Initial loan amount: $1$ , $600$ , $000$ rubles. Each January, the debt increases by $25$ %. Calculate the debt by January $2025$ . $\newline$ Calculation: $1,600,000 \times 1.25 = 2,000,000$ rubles.
Debt Calculation for January $2026$ : From February to April, Roman Matveevich makes equal payments. By January $2026$ , the debt should be the same as it was in January $2025$ after the payment. Calculate the debt by January $2026$ before the payment. $\newline$ Calculation: $2,000,000 \times 1.25 = 2,500,000$ rubles.
Total Payment by May $2027$ : The payments in $2025$ and $2026$ are equal, and by May $2027$ , the debt must be repaid in full. Calculate the total amount paid by May $2027$ . $\newline$ Calculation: $2,637.5 \times 1,000 = 2,637,500$ rubles.
Total Payments from $2025$ to $2027$ : Determine the total payments made from $2025$ to $2027$ . Since the payments in $2025$ and $2026$ are equal, and the debt is fully repaid by $2027$ , calculate the payment for each year. $\newline$ Calculation: $2,637,500 - 2,500,000 = 137,500$ rubles for $2027$ .