An investor wants to receive $1,000 dollars annually from two investments. He has put $4,500 in money market account 4% annual simple interest. How much should he invest in a stock fund that pays 10% annual simple interest to achieve this goal?
Set this up as an equation.
(4500*.1)+(.1*x)=1000
solve for x to get your answer.
Thank you very much!
Oops, I made a mistake..
(4500*.04)+(.1*x)=1000
ok thanks for the correction, I appreciate that!
To determine how much the investor should invest in the stock fund, we can use the concept of simple interest.
Let's break down the problem step by step:
1. We know that the investor wants to receive $1,000 annually. This means that the total amount of interest generated from both investments should be $1,000.
2. The investor has already put $4,500 in a money market account that pays a 4% annual simple interest. To find the interest generated by this account, we can use the formula:
Interest = Principal * Rate
In this case, the principal is $4,500 and the rate is 4%. So the interest generated by the money market account would be:
Interest_MoneyMarket = $4,500 * 0.04
3. We can now determine how much should be invested in the stock fund. Let's denote it as x. The stock fund pays a 10% annual simple interest. Applying the same formula as before:
Interest_StockFund = x * 0.10
4. Since the combined interest from both investments should be $1,000, we can set up the equation:
Interest_MoneyMarket + Interest_StockFund = $1,000
$4,500 * 0.04 + x * 0.10 = $1,000
5. We can now solve this equation for x, which will give us the amount the investor should invest in the stock fund.
$180 + 0.10x = $1,000
0.10x = $1,000 - $180
0.10x = $820
x = $820 / 0.10
x ≈ $8,200
Therefore, the investor should invest approximately $8,200 in the stock fund to achieve the goal of receiving $1,000 annually from the two investments.