Question 1137936: You would like to have $6,000.00 in 7 years for a special vacation following graduation by making deposits at the end of each year in an annuity that pays 4% compounded annually.
How much money should you deposit at the end of every year?
How much of the $6,000.00 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 annual payment (deposit); r is the annual percentage yield presented as a decimal;
n is the number of deposits (= the number of years, in this case).
From this formula, you get for for the annual payment
P =  . (1)
Under the given conditions, FV = $6,000; r = 0.04; n = 7. So, according to the formula (1), you get for the annual payment
P =  = $759.66.
Answer. The necessary annual deposit value is $759.66.
Of the $6000, only 7*759.66 = 5317.62 dollars comes from deposit.
The rest 6000.00 - 5317.62 = 682.38 dollars comes from interest.
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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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