Cyndee wants to invest $50,000. Her financial planner advises her to invest in three types of accounts: one paying 4%, one paying 5 1 2 %, 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 $2475?

Question

Business

Judah Keith

15 February, 17:18

Cyndee wants to invest $50,000. Her financial planner advises her to invest in three types of accounts: one paying 4%, one paying 5 1 2 %, 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 $2475?

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Answers (1)

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Blaine Valencia · Answer 1

amount invested at 4% = $22,000

amount invested at 5.5% = $17,000

amount invested at 6% = $11,000

Explanation:

step 1:

A = amount at 4%

B = amount at 5.5%

0.5A = amount at 6%

step 2:

A + B + 0.5A = 50,000

1.5A + B = 50,000

0.04A + 0.055B + (0.06 x 0.5A) = 2,475

0.04A + 0.055B + 0.03A = 2,475

0.07A + 0.055B = 2,475

step 3:

1.5A + B = 50,000 ←←← multiply by - 0.055

0.07A + 0.055B = 2,475

-0.0825A - 0.005B = - 2,750

0.07A + 0.055B = 2,475

step 4:

-0.0125A = - 275

step 5:

A = - 275 / (-0.0125) = $22,000 = amount invested at 4%

0.5 x 22,000 = $11,000 = amount invested at 6%

33,000 + B = 50,000 ⇒ B = $17,000 = amount invested at 5.5%