SOLUTION: Find the time required for an investment of 5000 dallied to grow to 7300 at an interest rate of 7.5 percent per year, compounded quarterly

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Question 1196857: Find the time required for an investment of 5000 dallied to grow to 7300 at an interest rate of 7.5 percent per year, compounded quarterly

Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!


Given Data:
Present value:

Future value:

Rate of interest: %=
Number of periods per year;





take log of both sides







approximately years

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

The answer and the entire conception of the solution in the post by MathLover1 is INCORRECT.

The amount of money at the discretely compounded account is not a continuous exponential
function. The amount is changed discretely at the time moments, when the compounding is
performed, i.e. at the end of each compounding time interval.

THEREFORE, in order for the answer be consistent with the problem, the time of 5.1 years
MUST be rounded to the closest GREATER time of compounding.

In this problem, the obtained time 5.1 years must be rounded to 5 years and one quarter,
in order for the bank was in position to make the last compounding.

I almost 100 times saw in this forum, as the tutors incorrectly solve such problem,
mistakenly teaching students, that the amount at discretely compounding accounts
is a continuous function, while it is not so in reality.

And every time as I noticed it, I issued this my warning.

But some tutors at this forum ignore it, so I am in doubt, if they themselves are able to learn.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Find the time required for an investment of 5000 dallied to grow to 7300 at an interest rate of 7.5 percent per year, compounded quarterly 
In years, it's 5.09297724, or about 5 years, 1.116 months. However, this needs to be ROUNDED UP to the next
compounding period which is  or 5 years, 3 months, or in quarters: 5(4) + 1 = 21.

The other person who responded doesn't know any better and that's why she makes a mess of most of the problmes she responds to,

and never, ever makes an effort to correct herself. Maybe she feels she doesn't need to, because she knows it all! Who knows!!
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