A company's loan at the beginning of 2010 was M million yuan, with an annual interest rate of m. Starting from the end of the year, the annual repayment amount was a million yuan, and it was repaid exactly within 10 years.

Analysis: Read the question carefully, and according to the meaning of the question, set up the amount to be repaid each year, express the arrears in each year, and use the last year to list the equation to get the answer.

Solution:

The amount to be repaid in equal installments is a, and the loan amount is M, then

The amount owed in the next year is M? (1 m)-a

p>

Amount owed in year 2 (M? (1 m)-a)? (1 m)-a

Amount owed in year 3 [(M? (1 m)-a) ?（1 m)-a]?（1 m)-a

Arrearage in the 10th year [[[[[M?（1 m)-a]?（1 m)-a]? (1 m)-a]]? (1 m)-a]? (1 m)-a=0 (including 10 a)

Organize:

M( 1 m)^10-a(1 m)^9-a(1 m)^8-a(1 m)^7-……- a=0

M(1 m)^10 - a*(1-(1 m)^10)/(1-(1 m))=0，

a*(1-(1 m)^10)/(1-(1 m))=M(1 m)^10

∴a=Mm（1 m）^10/[(1 m)^10-1].