Question

Martina made deposits of $2,000 at the beginning of each year for four years. The rate she earned is 5% annually. What's the value of Marina's account in four years? A. $11,051.00 B. $9,051.20 C. $8,260.00 D. $8,260.20

Answer 1

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 .

$FV_{Annuity\ Due} = C\times \frac{(1+i)^{n}-1}{i}\times (i+1)$

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 .

$= \frac{5}{100}$

= 0.05

i = 0.05

n = 4

Putting all the values in the above formula

$FV_{Annuity\ Due} = 2000\times \frac{(1+0.05)^{4}-1}{0.05}\times (0.05+1)$

$FV_{Annuity\ Due} = 2000\times \frac{(1.05)^{4}-1}{0.05}\times (1.05)$

$FV_{Annuity\ Due} = 2000\times \frac{(1.05)^{4}-1}{0.05}\times (1.05)$

$FV_{Annuity\ Due} = 2000\times \frac{1.21551-1}{0.05}\times (1.05)$

$FV_{Annuity\ Due} = 2000\times \frac{0.21551}{0.05}\times (1.05)$

$FV_{Annuity\ Due} = 2000\times 4.3102\times (1.05)$

$FV_{Annuity\ Due} = \ 9051.42$

Therefore the value of Marina's account in four years is $ 9051.42 .

Option (B) is correct .

Answer 2

I think B. $9,051.20 is the answer