Question 1136172: Hi Tutors,
I am having trouble with this word problem.
Suppose you just had your first child and you want to begin immediately putting away for his first car. Assume that car will cost a total of $32,000 and that your child will begin driving at age 16.
a. How much will you need to put away each month at a rate of 5% in order to achieve that goal?
b. How much money will you have actually put into the account over the course of the 16 years?
c. How much did your investment actually earn you?
d. Do you think it was actually worthwhile to put the money into an investment account? Explain why
Answer by ikleyn(52914)   (Show Source):
You can put this solution on YOUR website! .
In order for the problem formulation be PRECISELY CORRECT, it should say that the account is compounded monthly
and the deposit is paid at the end of each month.
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 monthly payment (deposit); r is the monthly percentage yield presented as a decimal;
n is the number of deposits (= the number of years multiplied by 12, in this case).
From this formula, you get for for the monthly payment
P =  . (1)
Under the given conditions, FV = $32,000; r = 0.05/12; n = 16*12. So, according to the formula (1), you get for the monthly payment
P =  = $109.13.
ANSWER (a). The necessary monthly deposit value is $109.13.
ANSWER (b). 109.13*12*16 = 20,952.96 dollars.
ANSWER (c). 32000 - 20,952.96 = 11,047.04 dollars
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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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