Question 1208037: You deposit $400 each month into an account earning 8% interest compounded monthly.
a) How much will you have in the account in 15 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Answers:
(a) $138,415.29
(b) $72,000
(c) $66,415.29
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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 = 138415.29
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Explanation for part (b)
P = 400 dollars deposited each month.
n = 180 months
n*P = 180*400 = 72000 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 = 66415.29
Answer by ikleyn(52752)  (Show Source):
You can put this solution on YOUR website! .
This problem in the post is formulated INCORRECTLY.
Why ? - Because there are TWO classic/standard TYPES of annuities.
Ordinary annuity saving plan assumes that the deposits are made at the end of each month.
Annuity Due saving plan assumes that the deposits are made at the beginning of each month.
These different types annuities use different formulas and lead to different final amounts.
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An accurate formulation must define in its description, which annuity is considered.
It must say when the deposits are made: at the beginning of months or at the end of months.
Without it, the problem's formulation is INCOMPLETE.
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I noticed/pointed it at this forum many times, but without any visible outcome.
So, based on this my experience, I conclude, that to teach these persons
to write these problems correctly is the same as to hit wood with a stick.
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