Answered

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Cyndee wants to invest $50,000. Her financial planner advises her to invest in three types of accounts: one paying 3%, one
paying 5%, and one paying 6% simple interest per year. Cyndee wants to put twice as much in the lowest-yielding, least-risky
account as in the highest-yielding account. How much should she invest in each account to achieve a total annual return of
$2120?

Sagot :

sqdancefan

Answer:

  • $25,333.33 at 3%
  • $12000 at 5%
  • $12,666.67 at 6%

Step-by-step explanation:

Cyndee invests $50,000 in accounts earning 3%, 5%, and 6% annually, for a total annual return of $2120. She puts twice as much in the first account as in the third. You want to know the amount invested in each account.

Setup

Let x represent the amount invested in the third account. Then 2x is the amount invested in the first account, and (50000 -3x) is the amount invested in the second account. The total return is ...

  0.03(2x) +0.05(50000 -3x) +0.06(x) = 2120

Solution

Simplifying the equation gives ...

  -0.03x +2500 = 2120

  380 = 0.03x . . . . . . . . . . add 0.03x-2120

  12,666 2/3 = x . . . . . . . divide by 0.03

  2x = 25,333 1/3

  50000 -3x = 12,000

Cyndee should invest 25,333.33 at 3%, $12,000 at 5%, and $12,666.67 at 6%.

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