Question 1208037
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Answers:
(a) <font color=red>$138,415.29</font>
(b) <font color=red>$72,000</font>
(c) <font color=red>$66,415.29</font>


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Explanation for part (a)


If we had one deposit, then we'd use the compound interest formula.
However, we instead have a steady stream of deposits.
So we must use the future value of annuity formula.


That particular formula is
FV = P*( (1+i)^n - 1 )/i
where,
FV = future value = account balance at some point in the future
P = deposit amount per month
i = interest rate per month in decimal form
n = number of months


For this particular problem we have the following inputs
P = 400 
i = r/12 = 0.08/12, which I'll leave as a fraction
n = 12*15 = 180 months (equivalent to 15 years)


Let's find the future value.
FV = P*( (1+i)^n - 1 )/i
FV = 400*( (1+0.08/12)^180 - 1 )/(0.08/12)
FV = 138415.2886446 approximately
FV = <font color=red>138415.29</font>


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Explanation for part (b)


P = 400 dollars deposited each month.
n = 180 months
n*P = 180*400 = <font color=red>72000</font> dollars is the total amount you deposit over the 15 year timespan.


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Explanation for part (c)


To find the amount of total interest, subtract the previous results.
interest = (result of part A) - (result of part B)
interest = 138415.29 - 72000
interest = <font color=red>66415.29</font>
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