Answer:
B. $5762.15.
Step-by-step explanation:
We have been given that Joey plans to invest $2,000 at the end of every year for 3 years. The interest rate on the account is 2.05% compounding annually.
We will use present value formula to solve our given problem.
[tex]\text{Present value}=P*[\frac{1-(1+r)^{-n}}{r}][/tex], where,
[tex]P=\text{Periodic payment}[/tex],
[tex]r=\text{Rate per period in decimal form}[/tex],
[tex]n=\text{Number of periods}[/tex].
Let us convert our given rate in decimal form.
[tex]2.05\%=\frac{2.05}{100}=0.0205[/tex]
Upon substituting our given values in above formula we will get,
[tex]\text{Present value}=2000*[\frac{1-(1+0.0205)^{-3}}{0.0205}][/tex]
[tex]\text{Present value}=2000*[\frac{1-(1.0205)^{-3}}{0.0205}][/tex]
[tex]\text{Present value}=2000*[\frac{1-0.94093792}{0.0205}][/tex]
[tex]\text{Present value}=2000*[\frac{0.05906208}{0.0205}][/tex]
[tex]\text{Present value}=2000*2.88107688[/tex]
[tex]\text{Present value}=5762.15376\approx 5762.15[/tex]
Therefore, the present value of the investment will be $5762.15 and option B is the correct choice.
