Question 10 A bank loaned out $29,000, part of it at the rate of 13% annual interest, and the rest at 4% annual interest.

The total interest earned for both loans was $2,195.00. How much was loaned at each rate?

$11,500 was invested at 13%.

$17,500 was invested at 4%

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

In this question:

Loans totaling 29,000.

P was invested at 13%

29000 - P was invested at 4%.

First investment:

Principal P.

Interest 13% = 0.13.

One year, so t = 1.

So

Second investment:

Principal 29000 - P.

Interest 4% = 0.04.

One year, so t = 1.

So

The total interest earned for both loans was $2,195.00.

This means that

So

So we solve the following system:

$11,500 was invested at 13%.

29000 - 11500 = 17500

$17,500 was invested at 4%