Answer: the amount invested at 13% is $9748
the amount invested at 5% is $3420
Step-by-step explanation:
Let x represent the amount invested at 13%.
Let y represent the amount invested at 5%.
$13,168 is invested, part at 13 % and the rest at 5%. This means that
x + y = 13168
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering the amount invested at 13%,
P = x
R = 13%
T =1 year
I = (x × 13 × 1)/100 = 0.13x
Considering the amount invested at 5%,
P = y
R = 5%
T = 1 year
I = (x × 5 × 1)/100 = 0.05y
If the interest earned from the amount invested at
13% exceeds the interest earned from the amount invested at
5% by $1438.24, it means that
0.13x - 0.05y = 1438.24 - - -- - - - - -1
Substituting x = 13168 - y into equation 1, it becomes
0.13(13168 - y) - 0.05y = 1438.24
1711.84 - 0.13y - 0.05y = 1438.24
- 0.13y - 0.05y = 1438.24 - 1711.84
- 0.08y = - 273.6
y = - 273.6/- 0.08
y = 3420
x = 13168 - y = 13168 - 3420
x = 9748
=