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Daran just retired, and has $670,000 to invest. A very safe Certificate of Deposit (CD) account pays 1.5%, while a riskier bond fund pays 8.5% in interest. Daran figures he needs $40,000 a year in interest to live on. How much should he invest in each account to make enough interest while minimizing his risk? Round answers to the nearest dollar.

Respuesta :

sqdancefan

Answer:

  • bond: $427,857
  • CD: $242,143

Step-by-step explanation:

We can use the given interest rates and the investment and interest amounts to write an equation for the amount of interest Daran needs to earn.

Setup

Let b represent the amount Daran should invest in the bond fund (in thousands). Then 670 -x is the amount he will invest in the CD account. The total interest he wants to earn (in thousands) is ...

  0.085(b) +0.015(670 -b) = 40

Solution

Eliminating parentheses and collecting terms, we have ...

  0.07b +10.05 = 40

  0.07b = 29.95

  b = 427.857

Daran should invest $427,857 in the bond fund and $242,143 in the CD account.

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