Question

A bank loaned out $16,000, part of it at the rate of 8% per year and the rest at 16%

per year. If the interest received in one year totaled $2000, how much was loaned at
8%?

Answer 1

$7,000

Explanation:

Let x = the part of $16,000 that was lent at 8%.

Then 16,000 - x is the part that was lent at 16%.

The interest earned at 8% is 0.08x.

The interest earned at 16% is 0.16(16,000 - x).

The total interest earned is 0.08x + 0.16(16,000 - x).

The total interest earned was $2,000, so

0.08x + 0.16(16,000 - x) = 2000

Now we solve for x to find out the amount lent at 8%.

0.08x + 0.16(16,000 - x) = 2000

0.08x + 2560 - 0.16x = 2000

-0.08x + 2560 = 2000

-0.08x = -560

x = 7000

Answer: $7,000