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You deposit $300 at the end of each month into an account earning 8% interest
compounded monthly. Answer the following questions. Round answers to the nearest cent.
a) What will the value of the account be in 25 years?
b) How much money in total will you deposit into the account?
c) How much total interest will you earn?
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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 = 300; r = 0.08/12; n = 12*25 = 300.
So, according to the formula (1), you get at the end of the 25-th year
FV = = = $285,307.92.
Note that you deposit only 12*25*$300 = $90,000.
The rest, $285,307.92 - $90,000 = $195307.9184 is what the account earns/accumulates in 25 years.
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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.