MATH SOLVE

2 months ago

Q:
# How much money should be deposited today in an account that earns 3 % compounded semiannually so that it will accumulate to $ 8000 in three years?

Accepted Solution

A:

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]= 0.03r = 0.03t = 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.