Question 1173380: A mother wishes to set up a savings account for her son's education. She plans on investing $750 when her son is 6 months old and every 6 months thereafter. The account earns interest of 8 percent per year, compounded semiannually.
(a) To what amount will the account grow by the time of her son's 18th birthday?
(b) How much interest will be earned during this period?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
A mother wishes to set up a savings account for her son's education. She plans on investing $750 when her son is 6 months old
and every 6 months thereafter. The account earns interest of 8 percent per year, compounded semiannually.
(a) To what amount will the account grow by the time of her son's 18th birthday?
(b) How much interest will be earned during this period?
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It is a classic Ordinary Annuity saving plan. The general formula is
FV =  , (1)
where FV is the future value of the account; P is the semi-annual payment (deposit); r is the semi-annual
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 = 750; r = 0.08/2; n = 2*18 = 36. So, according to the formula (1), you get at the end of the 17-th year
FV =  =  = $58198.74. ANSWER to (a)
Note that the mother deposits only 2*18*$750 = $27,000.
The rest 58198.74 - 27000 = 31198.74 dollars is the INTEREST what the account earns/accumulates in 18 years. ANSWER to (b)
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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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