You have 750000 in an ira at the time you retire. You have the option of investing this money in two funds Fund A pays 2.7% annually and fund B pays 7.7% annually. How should you divide your money between fund A and fund B to produce an annual interest income of 47,750

$200000 should be invested in fund A.

$550000 should be invested in fund B.

Step-by-step 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