Gabriel just retired, and has $640,000 to invest

Question

Gabriel just retired, and has $640,000 to invest. A very safe Certificate of Deposit (CD) account pays 2.5%, while a riskier bond fund pays 8.5% in interest. Gabriel figures he needs $42,000 a year in interest to live on. How much should he invest in each account to make enough interest while minimizing his risk?

$
at 2.5%

$
at 8.5%

Round answers to the nearest dollar.

Answer 1

Let x = the amount of money deposited in the safer CD

Let y = the amount of money deposited in the riskier bond

x + y = 640,000     x = 640,000 - y

.025x + .085y = 42,000      Multiply both sides by 100 to get rid of the decimal points.

25x + 85y = 42,000,000

25(640,000 - y) + 85y = 42,000,000

16,000,000 - 25y + 85y = 42,000,000

60y = 26,000,000

y = $433,333

x = 640,000 - 433,333

x = $206,667