Question 752377
Question #a:  Initial value is $unknown and Tanya wants final value to be $1200.  


This is the growth for n compounding periods:
{{{A=p*(1+r)^n}}}, where r is the growth rate as a decimal or fraction for the compounding period.  A is amount resulting from growth, p is the initial amount invested.  


If 6.4% is the yearly rate, then the semi annual rate is HALF of that, or 3.2% for each semi annual period.


{{{A=p*(1+0.032)^n}}}
{{{1200=p(1.032)^n}}}
and we easily find that 2.5 years to invest is 5 compounding periods.
{{{highlight(1200=p(1.032)^5)}}}


How you do the rest of the computing is your choice, but with that exponential equation, isolating p is fairly simple.
{{{highlight(p=1200/((1.032)^5))}}}



To the nearest whole dollar, $1025



Question #b:
Here, the question asks for r.
The equation to use would be with values set this way-------
{{{1200=970(1+r)^5}}}, but to find the ANNUAL rate instead of this semi-annual based equation, you'll want to multiply r by 2; you will be looking for {{{2*r}}}.