Answer:
$7319.3 should be deposited today in an account so that it will accumulate to $8000 in three years.
Step-by-step explanation:
Formula for Compounded semiannually
[tex]Amount = P(1 +\frac{r}{2})^{2t}[/tex]
Where P is the principle , r is the rate of interest in the decimal form and t is the time in years.
Amount = $8000
3% is written in the decimal form.
[tex]= \frac{3}{100}[/tex]
= 0.03
r = 0.03
t = 3 years
Put in the formula
[tex]8000 = P(1 +\frac{0.03}{2})^{2\times 3}[/tex]
[tex]8000 = P(1 +0.015)^{6}[/tex]
[tex]8000 = P(1.015)^{6}[/tex]
[tex]P = \frac{8000}{(1.015)^{6}}[/tex]
[tex]P = \frac{8000}{1.093\ (Approx)}[/tex]
P = $7319.3
Therefore $7319.3 should be deposited today in an account so that it will accumulate to $8000 in three years.
