Answer: $200000 should be invested in fund A.
$550000 should be invested in fund B.
Explanation:
Let x represent the amount that should be invested in fund A.
Let y represent the amount that should be invested in fund B
You have 750000 in an ira at the time you retire. You have the option of investing this money in two funds. This means that
x + y = 750000
The formula for determining simple interest is expressed as
I = PRT/100
Considering the amount invested in fund A
P = $x
T = 1 year
R = 2.7℅
I = (x × 2.7 × 1)/100 = 0.027x
Considering the amount invested in fund B
P = $y
T = 1 year
R = 7.7℅
I = (y × 7.7 × 1)/100 = 0.077y
For fund A and fund B to produce an annual interest income of 47,750, it means that
0.027x + 0.077y = 47750 - - - - - - -1
Substituting x = 750000 - y into equation 1, it becomes
0.027(750000 - y) + 0.077y = 47750
20250 - 0.027y + 0.077y = 47750
- 0.027y + 0.077y = 47750 - 20250
0.05y = 27500
y = 27500/0.05
y = 550000
x = 750000 - 550000
x = 200000