Topic: AlgebraQuestion: You save $15,000.00. You place one-third in a savings account earning a 4.6% APR compounded annually. You then invest one-quarter of the remaining balance in a 3-year U.S. Treasury bond earning a 5.2%Currently, you have $15,000, which you wish to invest using two different investment products. First, you invest a third of your savings as $5,000 into a savings account with a 4 percent interest rate. 6 percent annual percentage rate (APR) in which the interest is compounded on an annual basis. The value of this investment after one year is therefore given by the compound interest formula; \( A = P(1 + \frac{r}{n})^{nt} \). Here, \( P = $5,000 \), \( r = 0. 046 \), \( n = 1 \) and \( t = 1 \), since it compounds annually. Substituting the values, after one year is; \( A = 5000 \times (1+0. 046) = $5230 \) Then you subtract one-quarter of the remaining $10,000, which equals $2,500, to purchase a 3-year U. S. Treasury bond or note with a 5 %. 2% annual interest. Using the compound interest formula it is also possible to determine the future value of this investment after, say, three years. Here, P = $2,500, r = 0. 052, n = 1, and t = 3 years. Therefore, the sum after 3 years is \( A = 2500 \times (1 + 0. 052)^3 \approx 2500 times 1 \). 1649 = $2,912. 25 \). Altogether, the savings account will generate $5,230 within one year and the Treasury bond will be valued at about $2,912. 25 for 3 years to show diversification where different investment and profit levels pull 25. The revelation of diversified investment operations was well demonstrated in the table that showed the level of different investment and profit levels after the sampling period of three years.
