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​Betsy, a recent​ retiree, requires ​$6,000 per year in extra income. She has ​$60,000 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 ​$6,000 in interest per​ year?



Answer :

$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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