Betsy needs to invest $32,000 in the B-rated bonds paying 13% interest and $28,000 in the certificate of deposit paying 3% interest.
Interest is calculated by multiplying the rate with the principal.
Let x = the amount Betsy will invest in the B-rated bonds paying 13% per annum. The remaining amount, $60,000-x , she will invest in the certificate of deposit paying 3% per annum.
We can express the earnings on these two investments, after converting the percentages to their decimal equivalents, as: 0.13x+0.03(60000-x) and this is to earn a total of $5,000
Now we can write the necessary equation to solve for x.
or, 0.13x+0.03(60000-x) = 5000
or, 0.13x+1800-0.03x = 5000
or, 0.1x+1800 = 5000
or, 0.1x = 3200
or, x = 32000
So Betsy needs to invest $32,000 in the B-rated bonds paying 13% interest and the remainder ($60,000-$32,000 = $28,000) in the certificate of deposit paying 3% interest to obtain $5,000 in interest per annum.
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