SOLUTION: An investment of $4950 earns 11%/a compounded semi-annually. How long will it take for the investment to grow to $9411?

Question 1174220: An investment of $4950 earns 11%/a compounded semi-annually. How long will it take for the investment to grow to $9411?
Found 3 solutions by greenestamps, ikleyn, Solver92311:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

annual interest rate: 11% = 0.11
periodic interest rate (twice a year): 5.5% = 0.055
periodic growth factor: 1+0.055 = 1.055

The value after n compounding periods is the initial investment, multiplied by the periodic growth factor n times.

You want to know how long it will take the original $4950 to grow to $9411:

The variable is in an exponent; so to solve algebraically you need to use logarithms.

Use a calculator....

Or an easy path to the numerical answer is by graphing the two functions and on a graphing calculator and find that they intersect at n=12.

Then remember that n=12 is the number of compounding periods; since the compounding is twice a year, the length of time required for the investment to grow to $9411 is 12/2 = 6 years.

Answer by ikleyn(52765)   (Show Source): You can put this solution on YOUR website!
.

9411 = = 1.901212 = log(1.901212) = 2t*log(1.055) t = = 6.000022. ANSWER. 6 years (rounded). I hope that I safely rounded the value of 6.000022 to 6 and the last compounding will be done)

Solved.

-------------------

To see many other similar 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.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Logarithms".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

Happy learning (!)

Answer by Solver92311(821)   (Show Source): You can put this solution on YOUR website!

Solve for

John

My calculator said it, I believe it, that settles it

From
I > Ø

RELATED QUESTIONS
How long will it take for an investment of $46,000 to grow to $48,600 if the investment... (answered by jorel1380)
If interest is earned at the rate of 5%, compounded annually, how long will it take an... (answered by addingup)
A sum of $2500, 000 earns interest at a rate of 12% per year compounded quarterly. How... (answered by ikleyn,solver91311)
A sum of $2500, 00 earns interest at a rate of 12% per year compounded quarterly. How... (answered by greenestamps,josgarithmetic,ikleyn)
A sum of $250,000 earns interest at a rate of 12% per year compounded quarterly. How long (answered by solver91311,ikleyn)
An investment of $3000 earns 3.5% compounded semi- annually. a) what is the amount of... (answered by Edwin McCravy)
Sum of $250,000 earns interest at a rate of 12% per year compounded quarterly. How long... (answered by Boreal)
1. How long will it take for an investment of $25,000 to double at an interest rate of 4% (answered by Fombitz)
An initial investment is made at 4.5% interest, compounded semi annually, how long will... (answered by ankor@dixie-net.com)