Question 1179507: treasury bill is a short term investment product backed by the Bank of Ghana on behalf of the government. When you buy one,you are essentially lending money to the government of Ghana.Treasury bills are one of the safest forms of investment in Ghana because they are backed by the government of Ghana and are considered risk-free. Upon maturity, the government will repay the amount it borrowed with the determined interest rate given at the time of the investment. With this information in mind, Mariana decided to invest her 24,500 cedis. She divided the money into three different accounts. At the end of 2020, she made 1,300 cedis in interest. The 91-days yield on each of the three accounts was 4%, 5.5% and 6%. If the amount of money in the 4% account was four times the amount of money in the 5.5% account, how much money did she initially placed in each account?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this problem step by step.
**1. Define Variables**
* Let 'x' be the amount invested in the 5.5% account.
* Amount invested in the 4% account: 4x
* Amount invested in the 6% account: 24500 - x - 4x = 24500 - 5x
**2. Set Up the Interest Equation**
* Interest from 4% account: 0.04 * 4x = 0.16x
* Interest from 5.5% account: 0.055 * x = 0.055x
* Interest from 6% account: 0.06 * (24500 - 5x) = 1470 - 0.3x
* Total interest earned: 0.16x + 0.055x + 1470 - 0.3x = 1300
**3. Solve the Equation**
* Combine like terms: -0.085x + 1470 = 1300
* Subtract 1470 from both sides: -0.085x = -170
* Divide both sides by -0.085: x ≈ 2000
**4. Calculate the Amount in Each Account**
* 5.5% account: x ≈ 2000 cedis
* 4% account: 4x ≈ 8000 cedis
* 6% account: 24500 - 5x ≈ 14500 cedis
**Answer:**
Mariana initially placed:
* **2000 cedis** in the 5.5% account.
* **8000 cedis** in the 4% account.
* **14500 cedis** in the 6% account.
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