Question 1152737
<font color=black size=3>
<font color=red>Answer: 1921.01 dollars</font>


======================================================
Work Shown:


To calculate simple interest, we use this formula: {{{i = P*r*t}}}
i = interest earned
P = principal = amount deposited or invested
r = interest rate in decimal form
t = time in years


If we add on the amount of interest earned (i) to the original principal (P), then we get the final amount in the account after t years
{{{deposit+interest = P+i = P+P*r*t = P*(1+r*t)}}}
The total amount, after interest is added, is then equal to some value A
Therefore, a much more useful equation is {{{A = P*(1+r*t)}}}


We have,
A = 1999 = desired target to save to
P = unknown, what we want to solve for
r = 0.0609, decimal form of 6.09%
t = 8/12 since 8 months = 8/12 years



Let's plug in the given values and solve for P
{{{A = P*(1+r*t)}}}


{{{1999 = P*(1+0.0609*(8/12))}}} Plug in A = 1999, r = 0.0609, and t = 8/12


{{{1999 = P*(1+0.0406)}}} Use your calculator for this step


{{{1999 = P*(1.0406)}}} Add


{{{1999/1.0406 = (P*(1.0406))/1.0406}}} Divide both sides by 1.0406


{{{1999/1.0406 = P}}} Simplify the right side


{{{1921.00711128196 = P}}} Use your calculator for this step. This value is approximate.


{{{P = 1921.00711128196}}} Flip both sides


{{{P = 1921.01}}} Round up to nearest penny


-----------------------------


If you place $1,921.01 in a CD at 6.09% for 8 months, then you earn
{{{i = P*r*t}}}


{{{i = 1921.01*0.0609*(8/12)}}}


{{{i = 77.993006}}}


{{{i = 77.99}}} amount earned in interest


So the total amount is {{{P+i = 1921.01+77.99 = 1999}}}


Or we can use the other equation we found
{{{A = P*(1+r*t)}}}


{{{A = 1921.01*(1+0.0609*(8/12))}}}


{{{A = 1999.003006}}}


{{{A = 1999}}}
We get the same result either way, which confirms P = 1921.01 is correct.


</font>