A factory needs a bank loan as start-up capital for technical transformation. There are two schemes: Scheme A has a one-time loan of 654.38+million yuan and a profit of 654.38+million yuan in the first year, with an annual increase of 30% over the previous year; Scheme B has an annual loan of 654.38 million yuan and a profit of 654.38 million yuan in the first year, 5,000 yuan more than the previous year. The service life of both schemes is 10 year, and the principal and interest are paid off in one lump sum. If the loan interest rate is 10%, which scheme is more profitable? Accurate to 1000 yuan

Reference data:1.1/kloc-0 = 2.594,1.310 =13.797.

Analysis:

Scheme A: Operating start-up capital A0 = 65438+ 10,000 yuan;

Year-end: a1= A0+1=10+1=1.

End of 10: an = a1(1+30%) (n-1) = > a10 =1(/kloc

Loan repayment:10 (1+10%)10 = 25.94.

Profit:116.74-25.94 = 90.8.

Scheme B: The operating start-up capital is A0 = 1 ten thousand;

Year-end: a 1=a0+ 1=2

The operating start-up fund is: a1+1= 30,000;

At the end of the second year: A2 = (a1+1)+[1+0.5 (2-1)] = 3+1.5 = 4.5.

The operating start-up capital is A2+1= 55,000 yuan;

At the end of the third year: a3 = a2+1+[1+0.5 (3-1)] = 7.5.

……

The operating start-up capital is A9+1;

End of the decade: a10 = a9+1+[1+0.5 (10-1)]

∴a 1=2,a2=4.5,a3=7.5,a4= 1 1,a5= 15,a6= 19.5,a7=24.5,a8=30,a9=36,a 10=42.5

Ten years * * * = 2+4.5+7.5+…+42.5 =192.5.

Loan repayment:1(1+10%)1(1+10%) 9+…+1(1)

Profit:192.5-17.53 =174.97.

Obviously, the second option is more profitable.