Ex 2 brenda invests $5000 into an account that offered 3.4% interest compounded semi- annually. a) calculate the amount of money that brenda has in the account after 6 years. luke also invested $5000 into an account that offered r% interest compounded annually. after 6 years he had $6250 in his account. calculate r.

A] Brenda's amount after 6 years will be given by:
FV=P(1+r/100*n)^nt
where
P=principle amount
r=rate
n=number of terms
t=time 
thus
FV=5000(1+3.4/(2*100))^(2*6)
FV=5000(1.017)^12
FV=$6120.987
The amount of 6 years will be $6120.987

b. The rate at which Luke invested will be given by:
FV=p(1+r/100)^n
FV=$6250
p=5000
n=6 years
r=?
6250=5000(1+r/100)^6
solving for r we get
1.25=(1+r/100)^6
1.037891=1+r/100
0.037891=r/100
r=3.7891%