Question

Betsy, a recent​ retiree, requires ​$5000 per year in extra income. She has ​$60000 to invest and can invest in​ B-rated bonds paying ​13% per year or in a certificate of deposit​ (CD) paying ​5% per year. How much money should be invested in each to realize exactly ​$5000 in interest per​ year?

Answer 1

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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