Answer: $31000 was loaned at 13%.
Step-by-step explanation:
Let x represent the amount loaned out at 13% interest rate.
Let y represent the amount loaned out at 5% interest rate.
The bank loaned out $68,000, part of it at the rate of 13% per year and the rest at a rate of 5%per year. It means that
x + y = 68000
The interest received made from $x in one year is
13/100 × x = 0.13x
The interest received made from $y in one year is
5/100 × x = 0.05y
If the interest received was $5880, it means that
0.13x + 0.05y = 5880- - - - - - - - - 1
Substituting x = 68000 - y into equation 1, it becomes
0.13(68000 - y) + 0.05y = 5880
8840 - 0.13y + 0.05y = 5880
- 0.13y + 0.05y = 5880 - 8840
- 0.08y = - 2960
y = - 2960/- 0.08
y = 37000
x = 68000 - y = 68000 - 37000
x = $31000
