Answer:
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.
<em>Step 1: Determine loan amount at 9%</em>
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.
<em>Step 2: Determine loan amount at 11%</em>
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
