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"#
