The future value of $1,000 invested at 8% compounded semiannually for five years is [tex]\bold{\$ 1,480}[/tex]
Solution:
[tex]\bold{A = P (1 + i )^{n}}[/tex] ----------- equation 1
A = future value
P= principal amount
i = interest rate
n = number of times money is compounded
P = 1000
i = 8 %
[tex]\mathrm{n} = \text { compounding period } \times \text {number of years}[/tex]
(Compounding period for semi annually = 2)
[tex]\mathrm{n} = \text { compounding period } \times \text {number of years}[/tex]
Dividing “i” by compounding period
[tex]i = \frac{8 \%}{2} = 0.04[/tex]
Solving for future value using equation 1
[tex]\begin{array}{l}{A = 1000(1 + 0.04)^{10}} \\\\ {=1000 (1.04)^{10}}\end{array}[/tex]
[tex]= 1480.2[/tex]
[tex]\approx 1,480 \$[/tex]
