Question 883555
How is the interest compounded?
 
YEARLY COMPOUNDING:
If you deposit $5,500 and interest is 6.8% compounded yearly,
you would have $6,700.03 after 3 years.
Each year, interest would be added amounting to 6.8% of the balance at the start of the year.
Starting with $ {{{P}}} , with a rate of {{{r="6.8 %"=0.068}}} ,
you would get {{{P*r}}} added as interest at the end of the year,
for a total new balance of {{{P+P*r=P(1+r)=5500*1.068=5874}}} .
The next year, the process repeats, but now the whole ${{{5874=P(1+r)}}} is earning interest.
Again, you end the year with {{{(1+r)=1.068}}} times the starting balance,
so you end the second year with {{{P(1+r)^2=5874*1.068=about3273.43}}} .
The third year you end up with {{{P(1+r)^3=about}}}{{{3273.43*1.068=about6700.02}}} .
In general, after 3 years, you have earned a total of ${{{I}}} interest, and
{{{P+I=P*(1+r)^3}}} , so
{{{(P+I)/P=(1+r)^3}}} , so in this case
{{{(5500+1200)/5500=6700/5500=(1+r)^3}}}--->{{{1+r=root(3,6700/5500)=1.068}}} (rounded).
So {{{r=1.068-1=0.68="6.8 %"}}}