Question

A retiree has $200,000 to invest and needs to make $13,000 with her investments. If she can invest in government bonds at 6% or investment grade bonds at 8%, how much should she invest in each?

Answer 1

She should invest 150,000 in government bonds and 50,000 in investment grade bonds

Explanation:

Let the amount invested in government bonds be $y while the amount invested in investment bond be $x

Since total is $200,000

Then:

x + y = 200,000 ••••••(i)

Since 13,000 is what is expected to be earned, then this is like the interest.

thus;

6% of x + 8% of y = 13,000

6x/100 + 8y/100 = 13,000

Multiply through by 100

6x + 8y = 1300000 •••••••(ii)

From i, x = 200,000 - y

insert this into ii

6(200,000-y) + 8y = 1300000

1200000-6y + 8y = 1300000

2y = 1300000-1200000

2y = 100,000

y = 100,000/2

y = 50,000

but x + y = 200,000

thus, x = 200,000 - 50,000

x = 150,000