Formula shown below can be used to calculate the number of years to acquire the given "future value"=$10,800 with an interest rate that is compounded semi-annually; hence,
FV=P(1+i)^n
where:
FV="future value"=$10,800
P="principal"=$4,000
i="interest rate; semi-annual"=(5.25%)/(2)=2.625%=0.02625
n="number of years; semi-annual"=nxx2=2n
Now. plug in given data to find the n as shown;
FV=P(1+i)^n
$10,800=$4,000(1+0.02625)^(2n)
(1.02625)^(2n)=($10,800)/($4,000)
(1.02625)^(2n)=2.7, ( using the natural logarithm this can be presented as)
2nln1.02625=ln2.7
2n=ln2.7/ln1.02625
2n=0.99325177301/0.02591138178
2n=38.332644
n~~19.2" years"
