Question 1174589: You would like to have $41,000 in 5 years for the down payment on a new house following college
graduation by making deposits at the end of every three months in an annuity that pays 4.25%
compounded quarterly. How much should you deposit at the end of every three months? How
much of the $41,000 comes from deposits and how much comes from interest?
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
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 factual 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 quartely payment
P =  . (1)
Under the given conditions, FV = $41,000; r = 0.0425/4; n = 5*4. So, according to the formula (1),
you get for the quarterly payment
P =  = $1850.73.
In all. you deposit 5*4*1850.73 = 37014.60 dollars to the account.
The rest, the complement to $41,000, 41000 - 37014.60 = 3985.40 dollars is the interest.
Answer. The necessary quartely deposit value is $1850.73.
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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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