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Clark's younger brother saved $18 per month from his paper route for the past two years.
If interest is 4% compounded quarterly, how much will he have accumulated in his savings account?
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It is equivalently to say that Clark deposits 18*3 = 54 dollars at the end of every quarter
into the ordinary annuity, which provides 4% annually compounded quarterly.
So, apply the general formula for ordinary annuity future value
FV = , (1)
where FV is the future value of the annuity; P is the quarterly payment (deposit);
r is the quarterly effective percentage yield presented as a decimal;
n is the number of deposits (= the number of years multiplied by 4, in this case).
Under the given conditions, P = 18*3 = 54 dollars; r = 0.04/4 = 0.01; n = 2*4 = 8.
So, according to the formula (1), Clark's younger brother will get at the end of the 2-nd year
FV = = 447.43 dollars (rounded to the closest cent).
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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.