Question

Student borrowed 775,000. Some borrowed at 8%, 9% , 10%. How much borrowed at each interest rate if the annual interest was 67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%?

Answer 1

Average annual interest rate = 67500/775000=27/310
Let amount borrowed at 10% was x, then amount borrowed at 8% was 4x, and the amount borrowed at 9% was 775000-(x+4x)=775000-5x
Total interest
4x(.08)+x(0.10)+(775000-5x)(0.09)=67500
Isolate x and solve
-3x+6975000=6750000
3x=225000
x=75000 at 10%
So 4x=75000*4=300000 at 8%
775000-5x=775000-375000=400000 at 9%
Check:
300000*0.08+75000*0.10+400000*0.09=67500 (correct)