Question 1190272
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Part (a)


Future value of annuity formula
FV = P*( (1+i)^n - 1 )/i
where,
FV = future value
P = periodic deposit
i = interest rate per period
n = number of periods


In this case,
FV = 700,000
P = unknown monthly deposit
i = 0.07/12 = monthly interest rate
n = 12*30 = 360 months


Let's plug in the values mentioned and solve for P
FV = P*( (1+i)^n - 1 )/i
700,000 = P*( (1+0.07/12)^360 - 1 )/(0.07/12)
700,000 = P*1,219.97099577594
P = (700,000)/(1,219.97099577594)
P = 573.784132920946
P = 573.78
You need to deposit $573.78 per month, for 360 months, so that you end up with a future value of about $700,000.


Your teacher then states to round up to the nearest dollar. So we go from 573.78 to 574


Answer: <font color=red>$574</font>


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Part (b)


If you plugged P = 574, i = 0.07/12, and n = 360 into the future value annuity formula, then you'd get roughly FV = 700,263.35


We don't hit $700,000 exactly, but instead go over a bit. 
The alternative is that if P = 573, then FV would be somewhat shy of the 700 thousand dollar goal.
So this is why we rounded up.


Ignore the interest portion for now.
If you made 360 deposits of $574 each, then you paid 360*574 = 206,640 dollars into the account.


The total interest is the difference of the results we got
700,263.35 - 206,640 = 493,623.35


Answer: <font color=red>$493,623.35</font>
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