An investor has $45000 to invest in three types of accounts. Account A pays 4% annually Account B pays 6% and Account C pays 8%. The investor wishes to have a total return of $3000 on the investment with equal amounts invested in Account B and Account C. How much should be invested in each type of account to satisfy the investor's wishes? Round to the nearest hundredth.
A) Account A = $15000 Account B = $15000 Account C = $15000
B) Account A = $25000 Account B = $1000 Account C = $10000
C) Account A = $5000 Account B = $20000 Account C = $20000
D) There are infinitely many solutions
E) No solution

Question

Quizplus · Accepted Answer

Let x be the amount invested in Account A.
Then, the amount invested in Account B and Account C will each be $15,000 - (x/2) because the investment in these accounts is equal.

The total return from the investment is the sum of the returns from each account:
0.04x + 0.06($15,000 - x/2) + 0.08($15,000 - x/2) = $3,000

Simplifying and solving for x, we get:

0.04x + 900 - 0.03x = $3,000 - 1,200
0.01x + 900 = $1,800
0.01x = $900
x = $9,000

Therefore, the amount invested in each type of account is:
Account A = $5,000
Account B = $20,000 - ($9,000/2) = $15,500
Account C = $20,000 - ($9,000/2) = $15,500

Rounding to the nearest hundredth, we get:
Account A = $5,000
Account B = $15,500
Account C = $15,500

Therefore, the best choice is C.

An Investor Has $45000 to Invest in Three Types of Accounts