Answer:
The value of Marina's account in four years is $ 9051.42 .
Option (B) is correct .
Step-by-step explanation:
Formula for future value of annuity .
[tex]FV_{Annuity\ Due} = C\times \frac{(1+i)^{n}-1}{i}\times (i+1)[/tex]
Where C is the cash flow per period , i is the rate of interest and n is the number of payments .
As given
Martina made deposits of $2,000 at the beginning of each year for four years. The rate she earned is 5% annually.
C = $2000
5% is written in the decimal form .
[tex]= \frac{5}{100}[/tex]
= 0.05
i = 0.05
n = 4
Putting all the values in the above formula
[tex]FV_{Annuity\ Due} = 2000\times \frac{(1+0.05)^{4}-1}{0.05}\times (0.05+1)[/tex]
[tex]FV_{Annuity\ Due} = 2000\times \frac{(1.05)^{4}-1}{0.05}\times (1.05)[/tex]
[tex]FV_{Annuity\ Due} = 2000\times \frac{(1.05)^{4}-1}{0.05}\times (1.05)[/tex]
[tex]FV_{Annuity\ Due} = 2000\times \frac{1.21551-1}{0.05}\times (1.05)[/tex]
[tex]FV_{Annuity\ Due} = 2000\times \frac{0.21551}{0.05}\times (1.05)[/tex]
[tex]FV_{Annuity\ Due} = 2000\times 4.3102\times (1.05)[/tex]
[tex]FV_{Annuity\ Due} = \$ 9051.42[/tex]
Therefore the value of Marina's account in four years is $ 9051.42 .
Option (B) is correct .
