How do I solve for loan amount if I only have the annual interest?

Question

A company took a start up loan at 5% interest. They also took a capital improvement loan for 7% interest.  The start up loan is 8 times bigger than the improvement loan.

The interest paid on both loans for one year is 9,400. How do I determine how much the company borrowed for each loan?

 

Answer 1

This type of problem recurs over and over in these questions. The idea is to express the words in terms of equations. Here is a simple example:

Jack invests $1,000 is two investments, one yielding 5% per year and the other yielding 7% per year. At the end of one year he earned $63 of interest. How much was invested in each account?.

Let A = the account that earns 5% and B the account that earns 7%

A + B = 1,000
and
.05A + .07B = 63

Now express A in terms of B in the first equation and substitute in the second equation.
A = 1,000 – B
.05*(1,000 – B) + .07B = 63

50 – .05B + .07B = 63
.02B = 13
B = 13 / .02 = 650

Now that you know B you can use the fist equation to find A. Use A and B in the second equation to prove that the total amount of interest earned is 63.

In your problem the first equation is S = 8C, where S is the start-up loan and C the capital loan. S S is already defined in terms of C and that's what you use in the second equation. You should find that C = 20,000