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Jimmy wants to save $2000 in 3 years for a down payment on a motorcycle.
If he can earn 4% compounded quarterly, how much will he need to deposit
each quarter in order to save this amount?
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It is a classic Ordinary Annuity saving plan. The general formula is
FV = ,
where FV is the future value of the account; P is the quarterly payment (deposit);
r is the effective quarterly rate presented as a decimal;
n is the number of deposits (= the number of years multiplied by 4, in this case).
From this formula, you get for the quarterly payment
P = . (1)
Under the given conditions, FV = $2,000; r = 0.04/4 = 0.01; n = 3*4 = 12.
So, according to the formula (1), you get for the quarterly payment
P = = $157.70.
Answer. The necessary quartely deposit is $157.70.
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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.