A total of $28,000 is invested in two municipal bonds that pay 4.25% and 4.75% simple interest. The investor wants an annual interest income of $1250 from the investments. What amount should be invested in the 4.25% bond?

$16000 should be invested in the 4.25% bond.

Step-by-step explanation:

Let x represent the amount that he should invest in the bond paying 4.25 % interest.

Let y represent the amount that he should invest in the bond paying 4.75% interest.

A total of $28,000 is invested in two municipal bonds that pay 4.25% and 4.75% simple interest. This means that

x + y = 28000

The formula for determining simple interest is expressed as

I = PRT/100

Considering the bond paying 4.25% interest,

P = $x

T = 1 year

R = 4.25℅

I = (x × 4.25 × 1)/100 = 0.0425x

Considering the bond paying 4.75% interest,

P = $y

T = 1 year

R = 4.75℅

I = (y × 4.75 × 1)/100 = 0.0475y

The investor wants an annual interest income of $1250 from the investments. it means that

0.0425x + 0.0475y = 1250 - - - - - - 1

Substituting x = 28000 - y into equation 1, it becomes

0.0425(28000 - y) + 0.0475y = 1250

1190 - 0.0425y + 0.0475y = 1250

- 0.0425y + 0.0475y = 1250 - 1190

0.005y = 60

y = 60/0.005

y = 12000

x = 28000 - 12000 = $16000

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