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Question 1206511: You make semiannual deposits of $398
into an ordinary annuity earning 6.8%
compounded semiannually.
How much money is in the account after 11
years?
How much interest did you earn in your first year?
Answer by ikleyn(52770)   (Show Source):
You can put this solution on YOUR website! .
You make semiannual deposits of $398 into an ordinary annuity earning 6.8% compounded semiannually.
(a) How much money is in the account after 11 years?
(b) How much interest did you earn in your first year?
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It is a classic Ordinary Annuity saving plan (deposits are made at the end
of each semiannual period). The general formula is
FV =  , (1)
where FV is the future value of the account; P is the semiannual payment (deposit);
r is the nominal semiannual percentage yield presented as a decimal;
n is the number of deposits (= the number of years multiplied by 2, in this case).
Under the given conditions, P = 398; r = 0.068/2 0.034; n = 2*11 = 22.
So, according to the formula (1), the account after 11 years will be
FV =  =  = $12,720.32. Answer to (a)
The interest earned in the first year is
 = 13.53 dollars. ANSWER to (b)
Solved.
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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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