Last year, a women's professional organization made two small-business loans totaling $23,000 to young women beginning their own businesses. The money was lent at 9% and 11% simple interest rates. If the annual income the organization received from these loans was $2,430, what was each loan amount?

a. Loan amount at 9%=5,000

b. Loan amount at 11%=$18,000

Explanation:

To determine the amount of each loan amount, first we need to derive the following equations;

a.

Step 1: Determine loan amount at 9%

Total Interest=Interest from 9%+interest from 11%

where;

Total interest=$2,430

Interest from 9%=principal amount at 9%*interest rate*number of years

Interest from 11%=principal amount at 11%*interest rate*number of years

and;

Principal amount at 9%=x, interest rate=9/100=0.09, number of years=1

Principal amount at 11%=23,000-x, interest rate=11/100=0.11, number of years=1

replacing;

2,430 = (x*0.09*1) + 0.11 (23,000-x)

2,430=0.09 x+2,530-0.11 x

(0.11 x-0.09 x) = 2,530-2,430

0.02 x=100

x=100/0.02

x=5,000

Loan amount at 9%=5,000

b.

Step 2: Determine loan amount at 11%

Use the expression below to determine the loan amount at 11%;

Loan amount at 11%=Total loan amount-loan amount at 9%

where;

Loan amount at 11%=unknown, to be determined

Total loan amount=$23,000

Loan amount at 9%=$5,000

replacing;

Loan amount at 11%=23,000-5,000=$18,000

Loan amount at 11%=$18,000