Question

When she graduates college,Linda will owe 43,000 in student loans. The interest rate on the federal loans is 4.5 and the rate on the private bank loan is 2%. The total interés she owes for a year was 1,585. What is the amount of each loan

Answer 1

The amount of loan from federal is 29,000 and amount of loan from private bank is (43,000 - 29,000) = 14,000

Explanation:

Data provided:

Total amount owed by Linda = 43,000

Interest rate on the federal loans = 4.5%

Interest rate on the private bank loans = 2%

Total interest = 1,585

let the amount loaned by federal loans be 'A'

Therefore,

The amount loaned by private bank = 43,000 - A

Now,

4.5% of A + 2% of (43,000 - A) = 1,585

or

0.045A + 0.02(43,000 - A) = 1,585

or

0.045A + 0.02 × 43,000 - 0.02A = 1,585

or

0.025A + 860 = 1,585

or

0.025A = 1,585 - 860

or

0.025A = 725

or

A = 29,000

Hence,

The amount of loan from federal is 29,000 and amount of loan from private bank is (43,000 - 29,000) = 14,000