Answer:
The interest rate on the $ 8, 000 investment is 9. 657 % = 9.66%
While the interest rate on the $ 15, 000 investment is 10.257% = 10.26%
Step-by-step explanation:
Generally, the formular for calculating simple interest, I is given by
I = (principal x rate x time) / 100
Let the the annual interest on the $8,000 investment be represented as I. While the rate is represented as R
Since the time is 1year, interest on the $8, 000 can be expressed as
I = ( 8000 x R × 1) ÷ 100
I = 8000R/100
I = 80R. ( eqn 1)
Also, let the annual interest on $15,000 investment be K and the rate be V
Since interest on $15, 000 is greater than that of the $8,000 by $685
K = I + 685
Also rate V is 0.6% higher than R
V = (R + 0.6)%
This the interest on the $15, 000 is expressed as
K = ( 15000 × V × 1) ÷ 100 (eqn 2)
Substitute for K and V in eqn 2
That is
I + 685 = ( 15000 x (R + 0.6) x 1) ÷ 100
I + 685 = 15000 (R + 0.6) ÷ 100
I + 685 = 150 (R + 0.6)
Open the bracket
I + 685 = 150R + 15 × 0.6
I + 685 = 150R + 9.
This is the same as
150R + 9 = I + 685. ( eqn 3)
Substitute eqn 1 into eqn 3
That is put
I = 80R in eqn 3
150R + 9 = 80R + 685
Collect like terms with R to one side
150R - 80 R = 685 - 9
70R = 676
R = 676 ÷ 70
R = 9.657 %
Recall that V = (R + 0.6)%
V = 10.257 %
Thus the interest rate on the $ 8, 000 investment is 9. 657 % = 9.66%
While the interest rate on the $ 15, 000 investment is 10.257% = 10.26%
