Question 830810
a) 7% anual interest compounded semiannually means that every 6 months
{{{"7 %"/2="3.5 %"}}} interest is added to the balance.
That is {{{"3.5 %"=3.5/100=0.035}}} times the balance
After 6 months, you have
${{{750+750*0.035}}}=${{{750*(1+0.035)}}}=${{{750*1.035}}} .
You started with $750, but the calculation is the same for any other number.
In 6 months the amount grows by a factor of {{{1.035}}} .
Six month later, at the 1 year mark, that ${{{750*1.035}}} amount gets multiplied times {{{1.035}}} again,
so after one year you have ${{{750*1.035^2}}}.
That multiplication times {{{1.035^2}}} happens every year, so after {{{t}}} years you have
${{{750*(1.035^2)^t}}}=${{{highlight(750*1.035^(2t))}}}
 
b) For {{{t=1}}} , the amount is {{{750*1.035^2=750*1.071225=highlight(803.42)}}} (rounded).
For {{{t=6}}} , the amount is {{{750*1.035^12=750*1.511069=highlight(1133.30)}}} (rounded).
For {{{t=10}}} , the amount is {{{750*1.035^20=750*1.989789=highlight(1492.34)}}} (rounded).
For {{{t=15}}} , the amount is {{{750*1.035^30=750*2.806794=highlight(2105.10)}}} (rounded).