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$37,500 should be invested in B-rated bonds and $22,500 should be invested in a certificate of deposit in order to realize exactly $6,000 in interest per year.
- The total amount to be invested is $60,000.
- We are given two options for investing the money.
- The money can be invested either in B-rated bonds, which pays 13% interest per year, or in a certificate of deposit (CD), which pays 5% interest per year.
- Let the amount to be invested in B-rated bonds be 'x'.
- The amount to be invested in a certificate of deposit equals 60,000-x.
- The requirement is to get an exact amount of interest that equals $6000.
- The total interest per year = 13% of 'x' + 5% of (60,000-x).
- 6,000 = 13x/100 + 5(60,000-x)/100.
- 6,00,000 = 13x + 5(60,000-x)
- 6,00,000 = 13x + 300,000-5x
- 6,00,000 = 8x + 300,000
- 8x = 300,000
- x = 300,000/8
- x = 37,500
- Now calculate the value of 60,000-x.
- 60,000-x = 60,000-37,500
- 60,000-x = 22,500
- Thus, the amount to be invested in B-rated bonds is $37,500 and the amount to be invested in a certificate of deposit is $22,500.
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