Question 1202733: 1) You're setting up an annuity
2) A car costs $92,200.
3) You've bought a house
4) In how many ways
5) In a certain card game
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
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Comment from student : My apologies. If I can limit the above to one question,
"You're setting up an annuity to save for retirement in 32 years.
The monthly deposit is to be $525, with an annual interest rate of 5.4%,
how much will you have when you retire?"
The answer i've come up with I believe is wrong, but it's $537,553.86
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My response:
As the problem is worded, printed and presented, it is incorrect.
To be correct, the problem must say that the deposits are made at the end of each month
and that the account is compound monthly.
So, although it is not said in the problem, I will assume that it is so.
It is a classic Ordinary Annuity saving plan. The general formula is
FV =  , (1)
where FV is the future value of the account; P is your monthly payment (deposit);
r is the monthly percentage yield presented as a decimal;
n is the number of deposits (= the number of years multiplied by 12, in this case).
Under the given conditions, P = 525; r = 0.054/12; n = 12*32 = 384.
So, according to formula (1), you get at the end of the 32-th year
FV =  =  = $537553.86. ANSWER
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On Ordinary Annuity saving plans, see the lessons
- Ordinary Annuity saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans
in this site.
The lessons contain EVERYTHING you need to know about this subject, in clear and compact form.
When you learn from these lessons, you will be able to do similar calculations in semi-automatic mode.
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To make such complicated calculations as they are in this problem,
you should have/use an appropriate calculator for such long formulas.
Ideal choice is MS Excel, if you have it in your computer.
Then you write a formula in a text editor, copy-paste it
into an Excel work-sheet cell and click "enter" - the result is ready
in the next second.
If you have no MS Excel in your computer, you may find similar
free of charge calculators in the Internet. One such calculator is
www.desmos.com/calculator
It allows you to do the same thing: you write a formula in a text editor,
copy-paste it into this calculator and click "enter" - the result is ready
in the next second.
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Comment from student : Thank you so much! The problem doesn’t me toon compounding or if the deposit is made
at the beginning or rather at the end of the month so I was confused about how to answer.
My response : I understand it perfectly.
From the distance of thousand miles, it is clear from the first glance
in the post, that the author, who created it, is unprofessional Math writer.
I feel sorry for students of such a teacher,
who will know nothing after learning from him.
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