Question 1201359: Find the time required for an investment of 5000 dollars to grow to 7100 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Your answer is t = ____ years
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52835)   (Show Source):
You can put this solution on YOUR website! .
Find the time required for an investment of 5000 dollars to grow to 7100 dollars
at an interest rate of 7.5 percent per year, compounded quarterly.
~~~~~~~~~~~~~~~~~~~~~~~~~
Use the formula for the quarterly compounded account
F =  (1)
where
F = future value
A = present value (the starting deposit)
r = annual interest rate expressed as a decimal
n = number of quarters
For the amount of $5000, compounded quarterly at 7.5%, the future value formula is
F = 
where n is the number of quarters.
Therefore, our equation to find "n" is
7100 =
Divide both sides by 5000
 =  ,
or
1.42 =  .
Take logarithm base 10 of both sides
log(1.42) = n*log(1.01875)
and find the number of quarters "n" using your calculator
n =  = 18.88 quarters.
Finally, round this value 18.88 quarters to the nearest greater integer number 19,
in order for the bank was in position to make the last compounding.
ANSWER. 19 quarters, or 4 years and 3 quarters (same as 4 years and 9 months).
Solved.
-------------------
To see many other similar (and different) solved problems, look into the lesson
- Problems on discretely compound accounts
in this site, and learn the subject from there.
After reading this lesson, you will tackle such problems on your own without asking for help from outside.
Answer by josgarithmetic(39623)  (Show Source):
You can put this solution on YOUR website! This seems to be another example of the same kind of question already answered more than once, yesterday. Study THOSE and figure out how this one works.
For this one, can you figure what is the QUARTERLY interest rate, and how many such compounding periods are needed, and convert into years?
|
|
|
