Question

If XYZ invested $5,800 today in an account that is expected to earn 3.2 percent per year, and she expects to make another investment in the same account in 3 years from today, then how much money does XYZ expect to invest in 3 years if she expects to have $15,000 in her account in 4 years from today

Answer 1

The answer is "$8,160.08".

Step-by-step explanation:

`A= \text{future value} = \$ 15,000 \\\\P= \text{present value}= \$ 5,800 \\\\r=\tex{rate} =3.2 \%\\\\n= \text{time in years} = 4`

Using formula:

`A=P(1+ (r)/(100))^n + \text{Investment in 3 years} * (1.032)\\\\15,000=5,800 (1+ (3.2)/(100))^4 + \text{Investment in 3 years} * (1.032)\\\\15,000=5,800 (1+ 0.032)^4 + \text{Investment in 3 years} * (1.032)\\\\15,000=5,800 (1.032)^4 + \text{Investment in 3 years} * (1.032)\\\\`

`15,000 = 5,800 * 1.13427612 +\text{Investment in 3 years} * (1.032)\\\\15,000=6,578.8015 + \text{Investment in 3 years} * (1.032)\\\\\text{Investment in 3 years} = ((15000-6578.8015))/(1.032)\\\\\text{Investment in 3 years} = (8,421.1985)/(1.032)\\\\\text{Investment in 3 years} = 8,160.07607\\\\ \text{Investment in 3 years} = 8,160. 08`